What is the area of the figure below?
A quadrilateral is drawn with its diagonals. The diagonals meet at a right angle and bisect each other. The top left part of one diagonal is 6 inches. The bottom left part of the other diagonal is 7.5 inches.
(1 point)
Responses
45 in.²
45 in.²
90 in.²
90 in.²
135 in.²
135 in.²
180 in.²
The area of the quadrilateral is 45 in².
The formula to calculate the area of a quadrilateral when we know the diagonal lengths and the angles they make is: Area = (1/2) x d1 x d2, where d1 and d2 are the diagonals.
In this case, one part of the diagonal is 6 inches and the other part is 7.5 inches. This means the total length of one diagonal is 6 + 7.5 = 13.5 inches.
Since the diagonals bisect each other at a right angle, they split the quadrilateral into four right-angled triangles.
Each triangle has a base of 13.5 inches and a height of 6 inches (half the length of the shorter diagonal). The area of one triangle is (1/2) x base x height = (1/2) x 13.5 x 6 = 40.5 in².
Since there are four triangles, the total area of the quadrilateral is 40.5 x 4 = 162 in². However, we need to consider that we counted the area twice, so we divide by 2 to get the final answer:
Area = 162 / 2 = 81 in²
Therefore, the area of the quadrilateral is 81 in².