Use the image to answer the question.
An illustration shows a parallelogram with top side as 7 centimeters. A perpendicular dotted line from the top left vertex to the bottom side is 12 centimeters. The perpendicular line makes one right angle symbol with the top side and two right angle symbols with the bottom side.
What is the area of the quadrilateral?
(1 point)
cm2
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The area of the quadrilateral can be calculated using the formula for the area of a trapezoid, which is (1/2) * (sum of the lengths of the parallel sides) * (height).
Since the perpendicular line divides the parallelogram into two trapezoids, we can calculate the area of each trapezoid separately and then add them together.
For the first trapezoid:
- Top side = 7 cm
- Bottom side = 12 cm
- Height = 12 cm
- Area = (1/2) * (7 + 12) * 12 = (1/2) * 19 * 12 = 114 cm^2
For the second trapezoid:
- Top side = 7 cm
- Bottom side = 12 cm
- Height = 7 cm
- Area = (1/2) * (7 + 12) * 7 = (1/2) * 19 * 7 = 66.5 cm^2
Therefore, the total area of the quadrilateral is 114 cm^2 + 66.5 cm^2 = 180.5 cm^2.