4.Question

Use the image to answer the question.

An illustration shows a parallelogram with the right side as 16 inches. A perpendicular dotted line from top right vertex to the left side is 12 inches. The perpendicular line makes one right angle symbol with right side and two right angle symbols with the left side.

What is the area of the quadrilateral?

_____ in.2

1 answer

To find the area of the quadrilateral, we can divide it into two triangles: a right triangle and a parallelogram.

The right triangle has a base of 12 inches and a height of 16 inches. The area of the right triangle is (1/2) * base * height = (1/2) * 12 * 16 = 96 square inches.

The parallelogram has a base of 12 inches and a height of 16 inches (same as the right triangle). The area of the parallelogram is base * height = 12 * 16 = 192 square inches.

The total area of the quadrilateral is the sum of the area of the right triangle and the area of the parallelogram: 96 + 192 = 288 square inches.

Therefore, the area of the quadrilateral is 288 in^2.
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