https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:areas/x06d55bfa213a79fd:area-of-planar-regions/v/area-of-planar-regions 2025-10-27T12:01:04.888258735Z Area of planar regions In this video, we explore the concept of area of planar regions—flat surfaces enclosed by boundaries in a plane. You'll learn what a planar region is, how its area is defined, and why congruent figures always have equal areas. We also discuss how to calculate the area of complex shapes made up of multiple planar regions, using intuitive visuals and step-by-step reasoning. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction to planar region 00:58 Area of a planar region 01:36 Congruent figures have equal areas 03:12 Finding area of planar regions formed by two or more planar regions Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Area of planar regions In this video, we explore the concept of area of planar regions—flat surfaces enclosed by boundaries in a plane. You'll learn what a planar region is, how its area is defined, and why congruent figures always have equal areas. We also discuss how to calculate the area of complex shapes made up of multiple planar regions, using intuitive visuals and step-by-step reasoning. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction to planar region 00:58 Area of a planar region 01:36 Congruent figures have equal areas 03:12 Finding area of planar regions formed by two or more planar regions Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/zlgqIItakOQ.mp4/zlgqIItakOQ.mp4 254 Areas 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 Areas https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:areas/x06d55bfa213a79fd:figures-on-the-same-base-and-between-the-same-parallels/v/figures-on-the-same-base-and-between-the-same-parallels 2025-10-27T12:01:04.888258735Z Figures on the same base and between the same parallels In this video, we explore the geometric concept of figures lying on the same base and between the same parallels. You will learn what this term means, how to identify such figures, and why they are important in geometry. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 01:20 Figures having same base and not between the same parallels 04:30 Figures not having the same base and are between the same parallels 04:30 Figures having the same base and are between the same parallels 08:10 Conditions for figures to have the same base and to be between the same parallels Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Figures on the same base and between the same parallels In this video, we explore the geometric concept of figures lying on the same base and between the same parallels. You will learn what this term means, how to identify such figures, and why they are important in geometry. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 01:20 Figures having same base and not between the same parallels 04:30 Figures not having the same base and are between the same parallels 04:30 Figures having the same base and are between the same parallels 08:10 Conditions for figures to have the same base and to be between the same parallels Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/qfn2y-2RrJM.mp4/qfn2y-2RrJM.mp4 513 Areas https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:areas/x06d55bfa213a79fd:parallelograms-on-the-same-base-and-between-the-same-parallels/v/parallelograms-on-the-same-base-and-between-the-same-parallels 2025-10-27T12:01:04.888258735Z Parallelograms on the same base and between the same parallels In this video, we explore a classic geometry theorem: Parallelograms on the same base and between the same parallels are equal in area. Starting with a clear introduction, we walk through a color-coded, step-by-step proof that makes the logic easy to follow and visually intuitive. We then extend the idea to parallelograms on equal bases between the same parallels, showing why they also have equal areas. Finally, we discuss the converse of the theorem—how equal-area parallelograms between the same parallels must lie on equal bases—and explain why it holds true. This lesson blends visual clarity with rigorous reasoning, perfect for learners who love geometry that makes sense and sticks. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 01:02 Proof of 'Parallelograms on the same base and between the same parallels have equal areas' 04:18 Parallelograms on the same base(or equal bases) and between the same parallels 05:13 Why is the converse of this theorem true as well? Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Parallelograms on the same base and between the same parallels In this video, we explore a classic geometry theorem: Parallelograms on the same base and between the same parallels are equal in area. Starting with a clear introduction, we walk through a color-coded, step-by-step proof that makes the logic easy to follow and visually intuitive. We then extend the idea to parallelograms on equal bases between the same parallels, showing why they also have equal areas. Finally, we discuss the converse of the theorem—how equal-area parallelograms between the same parallels must lie on equal bases—and explain why it holds true. This lesson blends visual clarity with rigorous reasoning, perfect for learners who love geometry that makes sense and sticks. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 01:02 Proof of 'Parallelograms on the same base and between the same parallels have equal areas' 04:18 Parallelograms on the same base(or equal bases) and between the same parallels 05:13 Why is the converse of this theorem true as well? Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/sbFoBLM3Ds0.mp4/sbFoBLM3Ds0.mp4 347 Areas https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:areas/x06d55bfa213a79fd:parallelograms-on-the-same-base-and-between-the-same-parallels/v/parallelogram-triangle-on-the-same-base-and-between-parallels 2025-10-27T12:01:04.888258735Z Parallelogram & Triangle on the same base and between parallels In this video, we explore a classic geometry result: a triangle and a parallelogram on the same base and between the same parallels have a special area relationship. Through a step-by-step proof, we show how the triangle’s area is exactly half that of the parallelogram. Using clear visuals and color-coded diagrams, this lesson makes the logic easy to follow and the geometry intuitive. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:45 Proof of theorem - A parallelogram and a triangle are on the same base and between the same parallels Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Parallelogram & Triangle on the same base and between parallels In this video, we explore a classic geometry result: a triangle and a parallelogram on the same base and between the same parallels have a special area relationship. Through a step-by-step proof, we show how the triangle’s area is exactly half that of the parallelogram. Using clear visuals and color-coded diagrams, this lesson makes the logic easy to follow and the geometry intuitive. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:45 Proof of theorem - A parallelogram and a triangle are on the same base and between the same parallels Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/h559C9afdx4.mp4/h559C9afdx4.mp4 227 Areas 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 Areas https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:areas/x06d55bfa213a79fd:triangles-on-the-same-base-and-between-the-same-parallels/v/triangles-on-the-same-base-and-between-the-same-parallels 2025-10-27T12:01:04.888258735Z Triangles on the same base and between the same parallels "In this video, we explore a key geometry theorem: Triangles on the same base and between the same parallels are equal in area. Starting with a clear introduction, we walk through a neat, color-coded proof that makes the logic easy to follow and visually intuitive. Then we extend the idea to triangles on equal bases between the same parallels, showing why they also have equal areas. Finally, we discuss the converse of the theorem—how equal-area triangles between the same parallels must lie on equal bases—and explain why it holds true. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:39 Proof of theorem - Triangles on the same base and between the same parallels 04:05 Triangles on the same base (or equal bases) and between the same parallels 04:44 Why is the converse of this theorem true as well? Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Triangles on the same base and between the same parallels "In this video, we explore a key geometry theorem: Triangles on the same base and between the same parallels are equal in area. Starting with a clear introduction, we walk through a neat, color-coded proof that makes the logic easy to follow and visually intuitive. Then we extend the idea to triangles on equal bases between the same parallels, showing why they also have equal areas. Finally, we discuss the converse of the theorem—how equal-area triangles between the same parallels must lie on equal bases—and explain why it holds true. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!Unit link 00:00 Introduction 00:39 Proof of theorem - Triangles on the same base and between the same parallels 04:05 Triangles on the same base (or equal bases) and between the same parallels 04:44 Why is the converse of this theorem true as well? Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Khan Academy https://cdn.kastatic.org/ka-youtube-converted/AzB3cl48KgE.mp4/AzB3cl48KgE.mp4 310 Areas https://www.khanacademy.org/math/revision-tg-math-class-9/x6c9499d6e7016acd:week-3/x6c9499d6e7016acd:areas/e/revision-areas-tg-class-9 2026-02-18T21:20:35.275198076Z Revision areas TG class 9 . Khan Academy exercise