Question
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
80 in.2
80 in. squared
112 in.2
112 in. squared
102 in.2
102 in. squared
140 in.2
140 in. squared
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To find the area of the quadrilateral, we can split it into two triangles. The dotted perpendicular line splits the quadrilateral into two right triangles.
The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.
For the triangle on the left side of the dotted line:
Area = 1/2 * 14 * 8 = 56 in^2
For the triangle on the right side of the dotted line:
Using Pythagorean theorem, we can find the base of this triangle:
14^2 + x^2 = 10^2
196 + x^2 = 100
x^2 = 100 - 196
x^2 = 96
x = √96
x = 9.8
Area = 1/2 * 9.8 * 8 = 39.2
Therefore, the total area of the quadrilateral is:
56 + 39.2 = 95.2
Hence, the correct answer is not listed, but the closest one is 102 in^2