The area of a triangle is calculated using the formula:

Figure 9 Area of a Triangle

The perimeter of a triangle is calculated using the formula:

P = side₁ + side₂ + side₃. (3-2)

The area of a traingle is always expressed in square units, and the perimeter of a triangle is always expressed in the original units.

Example:

Calculate the area and perimeter of a right triangle with a 9" base and sides measuring 12" and 15". Be sure to include the units in your answer.

Solution:

The perimeter of a parallelogram is calculated using the following formula:

P=2a+2b (3-4)

The area of a parallelogram is always expressed in square units, and the perimeter of a parallelogram is always expressed in the original units.

Example:

Calculate the area and perimeter of a parallelogram with base (b) = 4', height (h) = 3', a = 5' and b = 4'. Be sure to include units in your answer.

Solution:

A rectangle is a parallelogram with four right angles, as shown in Figure 11.

Figure 11 Rectangle

The area of a rectangle is calculated using the following formula:

A = (length) (width) = lw (3-5)

The perimeter of a rectangle is calculated using the following formula:

P = 2(length) + 2(width) = 21 + 2w (3-6)

The area of a rectangle is always expressed in square units, and the perimeter of a rectangle is always expressed in the original units.

Example:

Calculate the area and perimeter of a rectangle with w = 5' and l = 6'. Be sure to include units in your answer.

Solution:

Figure 12 Square

A square is a rectangle having four equal sides, as shown in Figure 12.

The area of a square is calculated using the following formula:

A = a² (3-7)

The perimeter of a square is calculated using the following formula:

A = 4a (3-8)

The area of a square is always expressed in square units, and the perimeter of a square is always expressed in the original units.

Example:

Calculate the area and perimeter of a square with a = 5'. Be sure to include units in your

answer.

Solution:

Circles

A circle is a plane curve which is equidistant from the center, as shown in Figure 13. The length of the perimeter of a circle is called the circumference. The radius (r) of a circle is a line segment that joins the center of a circle with any point on its circumference. The diameter (D) of a circle is a line segment connecting two points of the circle through the center. The area of a circle is calculated using the following formula:

The circumference of a circle is calculated using the following formula:

Figure 13 Circle

Pi () is a theoretical number, approximately 22/7 or 3.141592654, representing the ratio of the circumference to the diameter of a circle. The scientific calculator makes this easy by designating a key for determining .

The area of a circle is always expressed in square units, and the perimeter of a circle is always expressed in the original units.

Example:

Calculate the area and circumference of a circle with a 3" radius. Be sure to include units in your answer.

Solution:

Summary

The important information in this chapter is summarized below.

Shapes and figures of Plane Geometry Summary