Use the image to answer the question.
An illustration shows a parallelogram with bottom side as 14 inches. A perpendicular dotted line from the bottom right vertex to the top side is 3 inches. The perpendicular line is denoted by two right angle symbols.
What is the area of the quadrilateral?
(1 point)
in.2
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To find the area of the quadrilateral, we need to find the height of the parallelogram first.
Since the dotted line is perpendicular to the bottom side and is 3 inches long, it divides the parallelogram into two right triangles. Using the Pythagorean theorem, we can find the height of the parallelogram:
a^2 + b^2 = c^2
(3)^2 + h^2 = 14^2
9 + h^2 = 196
h^2 = 187
h ≈ 13.67 inches
Now that we have the height and the base of the parallelogram, we can find the area:
Area = base x height
Area = 14 inches x 13.67 inches
Area ≈ 191.38 in^2
So, the area of the quadrilateral is approximately 191.38 square inches.