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
180 in.²
To find the area of the figure, we need to find the lengths of both diagonals. Since the diagonals meet at a right angle and bisect each other, the quadrilateral can be split into four right triangles. The length of one leg of each right triangle is half the length of the diagonal.
Let's call the length of the diagonal 2x. Therefore, the length of one leg of each right triangle is x.
The top left part of one diagonal is 6 inches, so the length of one leg (x) is 6/2 = 3 inches.
Similarly, the bottom left part of the other diagonal is 7.5 inches, so the length of one leg (x) is 7.5/2 = 3.75 inches.
Since the diagonals bisect each other, their lengths must be equal. So, 2x = x.
Solving for x, we get x = 3.
Now we can find the length of the diagonals:
Diagonal 1 = 2x = 2(3) = 6 inches.
Diagonal 2 = 2x = 2(3.75) = 7.5 inches.
The area of the quadrilateral can be found by multiplying the lengths of the diagonals and dividing by 2:
Area = (6 inches)(7.5 inches)/2 = 45 square inches.
Therefore, the area of the figure is 45 in².