# Area

### Area Calculation for the ACT Math Exam

You will need to calculate the area of geometric shapes, such as circles, squares, triangles, and rectangles, for the test.

Have a look at the example that follows.

Problem 1:

A football field is 100 yards long and 30 yards wide. What is the area of the football field in square yards?

A. 130

B. 150

C. 300

D. 1500

E. 3000

The area of a rectangle is equal to its length times its width.

So you need to remember this formula for rectangles:

width × length

This football field is 30 yards wide and 100 yards long, we now we can substitute the values.

rectangle area = width × length

width × length = 30 × 100  = 3000

Problem 2:

In the figure above,  XY is 4 inches long and YZ is 5 inches long.

What is the area of triangle XYZ?

F. 4

G. 5

H. 6

J. 12

K. 20

In order to find the answer to this questions, you need this formula:

triangle area = (base × height) ÷ 2

However, the base length of the triangle described in the problem, which is line segment YZ, is not given.

So, we need to calculate the base length using the Pythagorean theorum.

According to the Pythagorean theorem, the length of the hypotenuse is equal to the square root of the sum of the squares of the two other sides.

42 + base length2 = 5

16 + base length2 = 5

Now square each side of the equation in order to solve for the base length:

16 + base length2 = 5

(√16 + base length2)2 = 52

16 + base length2 = 25

16 − 16 + base length2 = 25 − 16

base length2 = 9

base length2 = √9

base length = √9

base length = 3

Now solve for the area of the triangle:

triangle area = (base × height) ÷ 2

(base × height) ÷ 2 = (3 × 4) ÷ 2  =

12 ÷ 2 = 6

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