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HELP ME PLEASE

A composite figure is shown.

A five-sided figure with two parallel sides. The shorter one is 18 meters. The height of the figure is 12 meters. The portion from the vertex to the perpendicular height is 7 meters. The portion from a point to a vertical line created by two vertices is 5 meters.

Which of the following represents the total area of the figure?

288 m2
360 m2
416 m2
576 m2

1 Answer

3 votes
To find the total area of the composite figure, we need to break it down into smaller shapes, and then add up their areas.

The five-sided figure can be divided into a rectangle and a triangle. The rectangle has a base of 18 meters and a height of 12 meters, so its area is 18 x 12 = 216 square meters. The triangle has a base of 7 meters and a height of 12 meters, so its area is 0.5 x 7 x 12 = 42 square meters.

The other portion of the figure is a trapezoid. To find its area, we need to find the average of the two parallel sides (18 meters and 5 meters), which is (18 + 5) / 2 = 11.5 meters. The height of the trapezoid is 12 meters. The area of the trapezoid is 0.5 x (18 + 5) x 12 = 138 square meters.

Therefore, the total area of the composite figure is:

216 + 42 + 138 = 396 square meters

None of the answer choices are correct. The closest answer choice is 416 m2, but the actual answer is 396 m2.
User Ehpc
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