### Area Calculation for the 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 correct answer is E.**

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

**The correct answer is H.**

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.

√4^{2} + base length^{2} = 5

√16 + base length^{2} = 5

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

√16 + base length^{2} = 5

(√16 + base length^{2})^{2} = 5^{2}

16 + base length^{2} = 25

16 − 16 + base length^{2} = 25 − 16

base length^{2} = 9

√base length^{2} = √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

**Go Back to the Geometry Problems Page**

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