Act Math Practice

Plane Geometry Answer 4

Plane Geometry Answer 4:

4.

In the figure above, XY is 4 inches long and YZ is 5 inches long. What is the area of triangle CXYZ?

F. 4

G. 5

H. 6

J. 12

K. 20

The correct answer is H.

In order to calculate the area of a triangle, 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 tha base length using the Pythagorean theorum.

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

Ö4² + base length² = 5

Ö16 + base length² = 5

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

Ö16 + base length² = 5
(Ö16 + base length²)² = 5²
16 + base length² = 25
16 - 16 + base length² = 25 - 16
base length² = 9
Öbase length² = Ö9
base length = Ö9
base length = 3

Now solve for the area of the triangle:

triangle area = (base ´ height) ÷ 2
triangle area = (3 ´ 4) ÷ 2
triangle area = 12 ÷ 2
triangle area = 6

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