Question

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Find the area of the parallelogram.

A parallelogram has a lower side measuring 24 centimeters and a right side measuring 9 centimeters. A dashed vertical segment with endpoints on the upper and lower sides is 8 centimeters and meets the lower left vertex at a right angle.

Answer 1

To find the area of a parallelogram, we multiply the base (lower side) by the height.

In this case, the base is 24 cm and the height is 8 cm. To find the height, we can use Pythagoras' theorem:

h^2 = 9^2 - 8^2
h^2 = 81 - 64
h^2 = 17
h = sqrt(17)

Now we can find the area:

A = base x height
A = 24 cm x sqrt(17) cm
A ≈ 99.1 cm^2

Therefore, the area of the parallelogram is approximately 99.1 square centimeters.