Use the image to answer the question.
An illustration shows a parallelogram. The top side, slanted downward, is 10 inches. The left side is 14 inches. A dotted perpendicular line is drawn from top right vertex to the left side and labeled as 8 inches. It is denoted by one right angle symbol on the right and two right angle symbols on the left.
What is the area of the quadrilateral?
(1 point)
Responses
112 in.2
112 in. squared
80 in.2
80 in. squared
102 in.2
102 in. squared
140 in.2
140 in. squared
The area of the quadrilateral can be found by dividing it into two triangles and finding the areas of those triangles.
First, find the height of the quadrilateral by using the Pythagorean theorem:
Height = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 inches.
Then, find the area of the triangle on the left side (base of 14 inches and height of 6 inches):
Area = 0.5 * base * height = 0.5 * 14 * 6 = 42 square inches.
Finally, find the area of the other triangle:
Area = 0.5 * base * height = 0.5 * 10 * 6 = 30 square inches.
Therefore, the total area of the quadrilateral is 42 + 30 = 72 square inches.
So the correct answer is not provided in the options given.