What is the area of the figure below?
A parallelogram is shown. The slanted bottom side is 6 meters. The vertical right side is 14 meters. The right side is extended with a dashed segment to a dashed perpendicular horizontal segment from the top left vertex of the parallelogram. The dashed horizontal segment is 4.5 meters.
(1 point)
Responses
31.5 m²
31.5 m²
63 m²
63 m²
84 m²
84 m²
126 m²
To find the area of the parallelogram, we can use the formula A = base x height. The base of the parallelogram is the slanted bottom side, which is 6 meters. To find the height, we can use the right side extended with the dashed segment. This forms a right triangle. The base of the right triangle is the dashed horizontal segment, which is 4.5 meters, and the vertical right side is 14 meters.
Using the Pythagorean theorem, we can find the height of the parallelogram.
Height^2 = hypotenuse^2 - base^2
Height^2 = 14^2 - 4.5^2
Height^2 = 196 - 20.25
Height^2 = 175.75
Height ≈ 13.25 meters
Now we can calculate the area by multiplying the base and height:
A = 6 meters x 13.25 meters
A ≈ 79.5 square meters
Therefore, the area of the figure is approximately 79.5 m².