Question

Find the shaded area of the figure. Please help would really appreciate it

Answer 1

Answer:  120 square cm

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Work Shown:

Let,

• A = area of unshaded rectangle (the 6 by 10 rectangle)
• B = area of the unshaded triangle (that has the "8 cm" inside it)
• C = area of parallelogram
• D = shaded area = C - (A+B) = C - A - B

We can see that A = 60 since the rectangle has base 10 and height 6, so 10*6 = 60.

The upper horizontal part of the parallelogram is 10+8 = 18 cm long. This means the bottom horizontal part of the parallelogram is the same length. The bottom portion shows 9 cm until we reach the triangle. This means that 18-9 = 9 cm is the base of the unshaded triangle (that has the "8 cm" inside it).

That triangle has area of 0.5*base*height = 0.5*9*8 = 36 square cm. So B = 36

The parallelogram has base 18 cm and height 12 cm, so it has area of 18*12 = 216. This means C = 216

We can then finally compute the value of D

D = C - A - B

D = 216 - 60 - 36

D = 120 square cm