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Course: Praxis Core Math > Unit 1

Lesson 5: Geometry
Test prep
Praxis Core Math
Lessons
Geometry
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Perimeter, area, and volume | Lesson

Google Classroom

What are perimeter, area, and volume?

The perimeter, P, of a polygon is the total length around the polygon's edges. When we add up all the side lengths of a polygon, we get its perimeter. For the figure below, the perimeter is:
P=s1+s2+s3+s4
The area, A, of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas.
The volume, V, of an object is the amount of space that object occupies. Volume is measured in cubic units such as cubic centimeters.

What skills are tested?

  • Calculating the perimeter of a polygon
  • Calculating a side length given the perimeter
  • Calculating the area of a polygon
  • Calculating a length given the area
  • Calculating the volume of an object
  • Calculating a length given the volume

Which perimeter formulas are on the test?

For a
, each side has the same length, s. The formula is:
P=4s
For a
, two sides have length l, and two sides have width w. The formula is:
P=2(l+w)
With each formula, we can also calculate the side lengths when P is given. To do so, we:
  1. Write down the appropriate equation.
  2. Plug in known values.
  3. Solve for s, l, or w.

Which area formulas are on the test?

For a
, each side has the same length, s. The formula is:
A=s2
For a
, two sides have length l, and two sides have width w. The formula is:
A=lw
For a
, we're concerned with the base b and the height h. The formula is:
A=bh
For a
with base b and the height h, the formula is:
A=12bh
With each formula, we can also calculate one of the linear dimensions when A is given. To do so, we:
  1. Write down the appropriate equation.
  2. Plug in known values.
  3. Solve for the linear dimension.

Which volume formulas are on the test?

For a
with length l, width w, and height h, the formula is:
V=lwh
We can also calculate one of the linear dimensions when V is given. To do so, we:
  1. Write down the volume equation.
  2. Plug in known values.
  3. Solve for l, w, or h.

Your turn!

TRY: CALCULATING PERIMETER
What is the perimeter of the rectangle above?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

TRY: CALCULATING AREA
Triangle ABC is shown in the figure above. What is the area of triangle ABC ?
Choose 1 answer:

TRY: CALCULATING LENGTH FROM AREA
The base of a triangle is 6 inches long. If the area of the triangle is 12 square inches, what is the height of the triangle in inches?
Choose 1 answer:

TRY: CALCULATING VOLUME
The box for a board game is 11 inches long, 11 inches wide, and 3 inches tall. What is the volume of the box in cubic inches?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
cubic inches

Things to remember

ShapePerimeter (P) formula
P=4s
P=2(l+w)
ShapeArea (A) formula
A=s2
A=lw
A=bh
A=12bh
ShapeVolume (V) formula
V=lwh

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