Question

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

Answer 1

Answer:

  B.  60 ft²

Step-by-step 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.