Answer:
The area of the rectangle is 48
Step-by-step explanation:
We know that AE is 6 and ED is 8, since it forms a triangle, use the Pythagorean theorem to find AD, which is one side of the rectangle.
The Pythagorean theorem says that a^2 + b^2 = c^2.
a is AE, b is ED, and c is AD, so 6^2 + 8^2 = c^2, 36 + 64 = c^2, 100 = c^2, 10 = c, so AD is 10
The area of the triangle is half of AE times ED, so 1/2(6)(8) = 1/2(48) = 24, the area of the triangle is 24.
Since the area of a triangle is 1/2 of the base times the height, we can figure out the height:
A = 1/2bh, 24 = 1/2(10)h, 24 = 5h, 4.8 = h, so the height of the triangle (and rectangle) is 4.8.
The height of the triangle is also the height of the rectangle:
The area of the rectangle is 4.8*10 = 48
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