https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem 2023-05-23T10:21:00.469536483Z Intro to the Pythagorean theorem The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² = C². The hypotenuse is the longest side, opposite the right angle. Sal Khan video https://cdn.kastatic.org/googleusercontent/zm9lxg5aZkInLh29lDFE0ccgsSaxlQuzX0ogkP6IbAwcTeapeXzOpPLaFNmpA6WAoS_PhTCuQDrDMou_Wqr5Y4nf Intro to the Pythagorean theorem The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² = C². The hypotenuse is the longest side, opposite the right angle. https://cdn.kastatic.org/ka-youtube-converted/AA6RfgP-AHU.mp4/AA6RfgP-AHU.mp4 646 Mensuration https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/e/pythagorean_theorem_1 2026-03-10T06:50:36.944772689Z Use Pythagorean theorem to find right triangle side lengths Find the length of the hypotenuse or a leg of a right triangle using the Pythagorean theorem.   Ben Alpert exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/e/right-triangle-side-lengths 2025-12-29T14:34:21.667121593Z Right triangle side lengths Use the Pythagorean theorem to determine if the given side lengths could form a right triangle. Lindsay exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/e/use-area-of-squares-to-visualize-pythagorean-theorem 2026-03-28T08:54:34.587533774Z Use area of squares to visualize Pythagorean theorem Visualize the Pythagorean theorem and its converse using the area of squares. Lindsay exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pyth-theorem/v/pythagorean-theorem-with-right-triangle 2023-05-09T21:01:11.605979523Z Pythagorean theorem with isosceles triangle To find the value of a base (x) in an isosceles triangle, first split the triangle into two congruent right triangles by drawing an altitude. Then, use the Pythagorean theorem to create an equation involving x. Finally, solve the equation to find the unknown base, x. video https://cdn.kastatic.org/ka_thumbnails_cache/2c9f7c97-d91f-44cf-aca5-8f76cf54b1f8_1280_720_base.png Pythagorean theorem with isosceles triangle To find the value of a base (x) in an isosceles triangle, first split the triangle into two congruent right triangles by drawing an altitude. Then, use the Pythagorean theorem to create an equation involving x. Finally, solve the equation to find the unknown base, x. https://cdn.kastatic.org/ka-youtube-converted/TjOlZr_2uW4.mp4/TjOlZr_2uW4.mp4 228 Mensuration https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/e/use-pythagorean-theorem-to-find-area 2026-04-08T00:16:02.937952483Z Use Pythagorean theorem to find area Find the area of triangles and quadrilaterals by first using the Pythagorean Theorem to find missing side lengths. Lindsay exercise https://www.khanacademy.org/math/revision-term-1-mh-math-class-10/x041ca11815640a3a:week-2/x041ca11815640a3a:pythagoras-theorem/e/pythagorean-triplets 2025-02-13T04:57:25.728250847Z Pythagorean triplets Pythagorean triplets ashish exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/v/pythagorean-theorem-3 2023-06-02T19:09:07.369858129Z Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. Sal Khan video https://cdn.kastatic.org/googleusercontent/yu5zzccGvx1c9EkgqD5u-SX3Qt42CJ2BRnvfLfSYtExN8xzpTmsAD64vGZz5qoGjBvup3ST8TRsu258UWRd_mF0 Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. https://cdn.kastatic.org/ka-youtube-converted/T0IOrRETWhI.mp4/T0IOrRETWhI.mp4 180 Mensuration https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/v/pythagorean-theorem-1 2023-06-02T19:09:07.369858129Z Pythagorean theorem word problem: fishing boat If we assume that the mast of a boat is at a right angle to the deck, then we can model the length of a rope stretched between the mast and deck as the hypotenuse of a right triangle. Then we can use the Pythagorean theorem to relate the lengths. Sal Khan video https://cdn.kastatic.org/googleusercontent/22gCRD837Vkb33-KqU1EhKn7rrhfmSAOggXycJrnLu-4ybDkIdPgF5UamYIBtD50PDrdaiCJkz0Qod7i2HU-JJX1nQ Pythagorean theorem word problem: fishing boat If we assume that the mast of a boat is at a right angle to the deck, then we can model the length of a rope stretched between the mast and deck as the hypotenuse of a right triangle. Then we can use the Pythagorean theorem to relate the lengths. https://cdn.kastatic.org/ka-youtube-converted/JVrkLIcA2qw.mp4/JVrkLIcA2qw.mp4 272 Mensuration https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/e/pythagorean-theorem-word-problems--basic 2026-03-31T14:59:02.026924717Z Pythagorean theorem word problems Use the Pythagorean theorem to solve word problems. Lindsay exercise https://www.khanacademy.org/math/cc-third-grade-math/imp-geometry/imp-area-formula-intuition/v/transitioning-from-counting-to-multiplying-to-find-area-3rd-grade-khan-academy 2021-07-07T20:19:25Z Transitioning from unit squares to area formula Lindsay finds the area of a rectangle both by counting unit squares and multiplying side lengths.  Lindsay Spears video https://cdn.kastatic.org/googleusercontent/0TcMAODNL5pHqeAqhsBwYzmo6XYyHkphibtUWYy4rg3HTA4BYrsKdKuo5yQlLqLYsBbb_UyhIGiQJ8mAh5GudWhX Transitioning from unit squares to area formula Lindsay finds the area of a rectangle both by counting unit squares and multiplying side lengths.  https://cdn.kastatic.org/ka-youtube-converted/mu3HHCdYYtY.mp4/mu3HHCdYYtY.mp4 202 Mensuration https://www.khanacademy.org/math/cc-third-grade-math/imp-geometry/imp-area-formula-intuition/e/finding-area-by-multiplying 2021-06-30T20:49:36Z Transition from unit squares to area formula Find area of rectangles by multiplying side-lengths. Lindsay Spears exercise https://www.khanacademy.org/math/cc-third-grade-math/imp-geometry/imp-area-formula-intuition/v/rectangle-area-as-product-of-dimensions-same-as-counting-unit-squares 2021-07-07T20:19:26Z Counting unit squares to find area formula Sal uses unit squares to see why multiplying side-lengths can also find the area of rectangles.    Sal Khan video https://cdn.kastatic.org/googleusercontent/stlR2hLpfqUfhlaLA1rKy8H9zxDvxEGD6edqlv1x1mvDZt_TDdE-iide8P6i7NGR_cnNQdkRDwsjUpENXZzeGTc Counting unit squares to find area formula Sal uses unit squares to see why multiplying side-lengths can also find the area of rectangles.    https://cdn.kastatic.org/ka-youtube-converted/DRg2VCo8lP0.mp4/DRg2VCo8lP0.mp4 320 Mensuration https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-area-triangle/v/intuition-for-area-of-a-triangle 2023-06-30T00:54:25.287354524Z Area of a triangle The area of a rectangle and a parallelogram is found by multiplying the base by the height. For a triangle, the area is half of a parallelogram's, so it's calculated by multiplying the base by the height and then dividing by 2. video https://cdn.kastatic.org/googleusercontent/Fi9pR66SMMyijKzoyFIw6a2cHjUub-HncPLAlfT0a90llRBEciMFgGmv-CAlSSHoRNi9iIgUuqiBYzHBnwv9yt4 Area of a triangle The area of a rectangle and a parallelogram is found by multiplying the base by the height. For a triangle, the area is half of a parallelogram's, so it's calculated by multiplying the base by the height and then dividing by 2. https://cdn.kastatic.org/ka-youtube-converted/rRTXKQpblEc.mp4/rRTXKQpblEc.mp4 330 Mensuration https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-area-triangle/e/area-of-right-triangles 2026-04-08T00:16:02.937952483Z Area of right triangles Find the area of right triangles Lindsay exercise https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-area-triangle/e/area_of_triangles_1 2026-03-24T23:41:07.080866137Z Area of triangles Practice finding the area of right, acute, and obtuse triangles. Chanda Stanaland Johnson exercise https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/advanced-area-with-triangles/v/area-of-an-equilateral-triangle 2020-06-23T07:22:42Z Area of equilateral triangle Finding the formula for the area of an equilateral triangle with side s Sal Khan video https://cdn.kastatic.org/googleusercontent/lUjD7cst915kQlqm8ES0Pd4Axdx7mUlfpkMYlAY7shaS70Qu9wkHMOVPFOsPUAOWvG03FlM6z9t0gb1_VnV_WYmWDA Area of equilateral triangle Finding the formula for the area of an equilateral triangle with side s https://cdn.kastatic.org/ka-youtube-converted/UKQ65tiIQ6o.mp4/UKQ65tiIQ6o.mp4 222 Mensuration https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/heron-formula-tutorial/v/heron-s-formula 2020-08-25T18:06:03Z Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides Sal Khan video https://cdn.kastatic.org/googleusercontent/yoFDg3hgOeccTlrdVdadCkI70dwwbRa5rdjmKatYCkDVuLJRSfOYvwJCwj-wgmaTx5WD7zTb2gICFbPGqOoZZyM Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides https://cdn.kastatic.org/ka-youtube-converted/-YI6UC4qVEY.mp4/-YI6UC4qVEY.mp4 283 Mensuration https://www.khanacademy.org/math/class-9-geometry-od/x0a98afb01410c41a:mensuration/x0a98afb01410c41a:area-of-triangles/e/finding-area-of-triangle-using-heron-s-formula 2026-03-07T07:20:41.87360937Z Finding area of triangle using Heron's formula part 1 We will find the area of triangle using Heron's formula. anmol exercise https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-parallelogram-area/v/intuition-for-area-of-a-parallelogram 2023-06-30T00:54:25.287354524Z Area of a parallelogram Discover the magic of geometry! The area of a rectangle and a parallelogram can be calculated in the same way. Just multiply the base by the height! This simple trick works because a parallelogram can be rearranged into a rectangle. Geometry is full of surprises! video https://cdn.kastatic.org/googleusercontent/obiKP_sTiYrTr2fcbjLKQd_D2WPPutmNxH_iXMfLCXGMXZfuweYw8KyoZdldr2mQFrC5n9vLBH0H_xSehXBS4vEV Area of a parallelogram Discover the magic of geometry! The area of a rectangle and a parallelogram can be calculated in the same way. Just multiply the base by the height! This simple trick works because a parallelogram can be rearranged into a rectangle. Geometry is full of surprises! https://cdn.kastatic.org/ka-youtube-converted/hm17lVaor0Q.mp4/hm17lVaor0Q.mp4 177 Mensuration https://www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:cc-6th-plane-figures/cc-6th-parallelogram-area/e/area_of_parallelograms 2025-02-07T09:32:27.480992556Z Area of parallelograms Practice finding the area of parallelograms given base and height. Omar Rizwan exercise https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-quadrilaterals-theorems/v/proof-rhombus-area-half-product-of-diagonal-length 2021-02-16T16:08:13Z Proof: Rhombus area Sal proves that we can find the area of a rhombus by taking half the product of the lengths of the diagonals. Sal Khan video https://cdn.kastatic.org/googleusercontent/tAx2OHIpfuY5ZPgHnxPkPDD7sTS-b1wiePEMxwLKtkEfcnXauiufIaiz_VfNArV-w8Cm9PUFWgg0P15o8nenBxk Proof: Rhombus area Sal proves that we can find the area of a rhombus by taking half the product of the lengths of the diagonals. https://cdn.kastatic.org/ka-youtube-converted/3FManXv4mZM.mp4/3FManXv4mZM.mp4 307 Mensuration https://www.khanacademy.org/math/revision-term-1-od-math-class-9/x78c096538f3f5cab:week-3/x78c096538f3f5cab:mensuration/v/find-the-length-of-each-side-of-rhombus-when-diagonals-are-given 2025-07-15T06:45:11.189085042Z Find the length of each side of rhombus when diagonals are given Ever wondered how the diagonals of a rhombus relate to the length of its sides? This video unveils the simple formula you can use! We'll start with a practical example, then dive into the key properties of a rhombus and use the Pythagorean theorem to derive the formula from scratch. Follow along with solved problems to master this essential geometry skill. 🔷 Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Find the length of each side of rhombus when diagonals are given Ever wondered how the diagonals of a rhombus relate to the length of its sides? This video unveils the simple formula you can use! We'll start with a practical example, then dive into the key properties of a rhombus and use the Pythagorean theorem to derive the formula from scratch. Follow along with solved problems to master this essential geometry skill. 🔷 https://cdn.kastatic.org/ka-youtube-converted/W_42ifSDxgI.mp4/W_42ifSDxgI.mp4 507 Mensuration https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-area-trap-composite/v/area-of-a-trapezoid-1 2023-04-15T06:42:38.642148315Z Area of trapezoids Area of a trapezoid is found with the formula, A=(a+b)h/2. To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the "bases") and the height. Add the lengths of the two bases together, and then multiply by the height. Finally, divide by 2 to get the area of the trapezoid. Sal Khan video https://cdn.kastatic.org/googleusercontent/2Qf_I9kn1tNDqsjFdl-9bjcHfFsPAwH-C-Wl-UTQIxVSY-8daxkrR9NlhBsu4tE4JgvWXA32HaInnk33giWNBfC6 Area of trapezoids Area of a trapezoid is found with the formula, A=(a+b)h/2. To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the "bases") and the height. Add the lengths of the two bases together, and then multiply by the height. Finally, divide by 2 to get the area of the trapezoid. https://cdn.kastatic.org/ka-youtube-converted/j3-XYLnxJDY.mp4/j3-XYLnxJDY.mp4 288 Mensuration https://www.khanacademy.org/math/geometry-home/geometry-area-perimeter/geometry-area-trap-composite/e/areas_of_trapezoids_rhombi_and_kites 2026-03-24T23:41:07.080866137Z Area of trapezoids Practice finding the areas of trapezoids. Omar Rizwan exercise https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/x0267d782:cc-6th-nets-of-3d-figures/v/nets-of-polyhedra 2021-06-30T20:49:36Z Intro to nets of polyhedra Admittedly, "nets of polyhedra" sounds like the title of a bad sci-fi movie about man-eating, multi-headed fish. But in reality, nets of polyhedra are just 2D objects that wrap around 3D objects, like wrapping paper around presents. Sal Khan video https://cdn.kastatic.org/googleusercontent/Y37mID-JZzxDjs9nLIGVxHcULrvN-cPKP5AOM7ttIqnBJu8lHa-4qHJt_S0RYN7f2Pks_5Zm1JSVk6l4ZN6FILU Intro to nets of polyhedra Admittedly, "nets of polyhedra" sounds like the title of a bad sci-fi movie about man-eating, multi-headed fish. But in reality, nets of polyhedra are just 2D objects that wrap around 3D objects, like wrapping paper around presents. https://cdn.kastatic.org/ka-youtube-converted/ZACf9EecFrY.mp4/ZACf9EecFrY.mp4 408 Mensuration https://www.khanacademy.org/science/ap-biology/cell-structure-and-function/cell-size/v/surface-area-of-a-box 2022-11-16T04:22:43.7414897Z Surface area of a box (cuboid) Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Surface area of a box (cuboid) Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw. https://cdn.kastatic.org/ka-youtube-converted/1iSBNSYhvIU.mp4/1iSBNSYhvIU.mp4 145 Mensuration https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:surface-areas-and-volumes/x06d55bfa213a79fd:surface-area-of-cuboid-and-cube/e/b8-surface-area-of-cube-and-cuboid 2025-02-24T09:39:19.049669771Z Surface area of cube and cuboid Surface area of cube and cuboid ashish exercise https://www.khanacademy.org/math/tg-math-class-9-bridge/x5c093f69f2aa4d76:surface-area-and-volumes/x5c093f69f2aa4d76:volume-of-cube-and-cuboid/v/volume-unit-conversion 2025-07-15T05:11:54.70453665Z Volume Unit Conversion Confused about converting cubic units? This video breaks it down step by step! We start with the basic volume unit conversion chart and show you how to confidently convert between units like cubic centimeters, cubic meters, and cubic kilometers. Learn how to: Understand the standard volume units Use the conversion chart effectively Convert between cubic units with ease. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Volume Unit Conversion Confused about converting cubic units? This video breaks it down step by step! We start with the basic volume unit conversion chart and show you how to confidently convert between units like cubic centimeters, cubic meters, and cubic kilometers. Learn how to: Understand the standard volume units Use the conversion chart effectively Convert between cubic units with ease. https://cdn.kastatic.org/ka-youtube-converted/LjnK7-weuPg.mp4/LjnK7-weuPg.mp4 235 Mensuration https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/imp-finding-volume/v/volume-of-a-rectangular-prism-or-box-examples 2022-11-16T04:22:43.7414897Z Volume of a rectangular prism If you want to know how much stuff you can cram into a box, finding its volume is key. To calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions together. This formula works regardless of the units you are using (e.g. meters, feet), he method is the same - just make sure your units match up! Sal Khan video https://cdn.kastatic.org/googleusercontent/trl4HROL5F5JhCgGZyneiSc0I7-KAv7V6EEwtZlyAkchGk-QJPBYUbp1sScM0eQ803NUaaK8zcMyXcRrm8bDb5G1 Volume of a rectangular prism If you want to know how much stuff you can cram into a box, finding its volume is key. To calculate the volume of a box, you need to know its height, width, and depth. You can find the volume by multiplying these three dimensions together. This formula works regardless of the units you are using (e.g. meters, feet), he method is the same - just make sure your units match up! https://cdn.kastatic.org/ka-youtube-converted/I9efKVtLCf4.mp4/I9efKVtLCf4.mp4 119 Mensuration https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/imp-finding-volume/e/volume_1 2026-02-02T11:44:44.872808183Z Volume of rectangular prisms Find volume of a rectangular prism with labeled whole number side lengths. Sid Patel exercise