Answer:
- 18550 cm²
- 88 ft²
Step-by-step explanation:
1. There are several ways the area can be divided up so that formulas for common figures can be used to find the areas of the pieces. In the attached figure, we have identified an overall rectangle ABXE and a trapezoid BXDC that is subtracted from it.
The area of the rectangle is the product of length and width:
area ABXE = (180 cm)(140 cm) = 25,200 cm²
The area of a trapezoid is the product of its height (DX = 70 cm) and the average of its base lengths ((BX +DC)/2 = 95 cm).
area BXDC = (70 cm)(95 cm) = 6650 cm²
Then the area of figure ABCDE is the difference of these areas:
area ABCDE = area ABXE - area BXDC = (25,200 - 6,650) cm²
area ABCDE = 18,550 cm²
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2. In order to find the area of the figure, we need to know the length DE. That length is one leg of right triangle DEA, so we can use the Pythagorean theorem. That theorem tells us ...
DE² + EA² = AD²
DE² + (8 ft)² = (10 ft)² . . . . . substitute the given values
DE² = 36 ft² . . . . . . . . . . . . .subtract 64 ft²
DE = 6 ft . . . . . . . . . . . . . . . take the square root
Now, we can choose to add the area of triangle DEA to that of square ABCE, or we can treat the whole figure as a trapezoid with bases AB=8 ft and DC=14 ft. In the latter case, the average base length is ...
(8 ft + 14 ft)/2 = 11 ft
and the area is the product of this and the 8 ft height:
area ABCD = (11 ft)(8 ft) = 88 ft²
