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ABCD is a parallelogram; find the area of the shaded region.

A. 120 ft2

B. 60 ft2

C. 90 ft2

D. 150 ft2

ABCD is a parallelogram; find the area of the shaded region. A. 120 ft2 B. 60 ft2 C-example-1
User Rosalinda
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1 Answer

4 votes

Answer:

B. 60 ft²

Explanation:

The overall area of the parallelogram is the product of its base length (15 ft) and height (8 ft), so is ...

overall area = (15 ft)(8 ft) = 120 ft²

The area of the quadrilateral in the middle of the parallelogram is the area of two triangles, each with a base equal to 15 ft (the horizontal line in the diagram), and heights that total 8 ft. If we let x represent the height of one of those triangles, then the other has a height of (8-x) and the sum of their areas is ...

quadrilateral area = (1/2)(15 ft)(x) +(1/2)(15 ft)(8 ft -x)

= (1/2)(15 ft)(x + 8 ft - x) = (1/2)(15 ft)(8 ft) = 60 ft²

Then the shaded area is the difference between the parallelogram area and the quadrilateral area:

shaded area = parallelogram area - quadrilateral area

= (120 ft²) - (60 ft²)

= 60 ft²

The area of the shaded region is 60 ft².

User Vadim Beskrovnov
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