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Find the area of the shaded region. Round to the nearest hundredth where necessary. Remember: you are subtracting the areas.

Find the area of the shaded region. Round to the nearest hundredth where necessary-example-1

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Given:

The base of the given figure = 23.8 ft

Height of the parallelogram = 15 ft

To find the area of the shaded region.

Formula


  • A = A_(1) -A_(2)

where,
A be the area of the shaded region


A_(1) be the area of the parallelogram.


A_(2) be the area of the triangular part.

  • The area of triangle
    A_(2) = (1)/(2) bh where, b be the base and h be the height.
  • The area of the parallelogram
    A_(1) =( base)(height)
  • By Pythagoras theorem,
    hypotenuse^(2) = base^(2)+height^(2)

Now,

Putting, Base = 21, Hypotenuse = 23.8 we get,


Height^(2) = 23.8^(2)-21^(2)

or,
Height = √(566.44-441)

or,
Height = 11.2

Therefore,

Area of the parallelogram
A_(1) = (23.8)(15) sq ft = 357 sq ft

Area of the triangle
A_(2) =
(1)/(2)(11.2)(21) sq ft = 117.6 sq ft

So,

The area of the shaded part = (357-117.6) sq ft = 239.4 sq ft

Hence,

The area of the shaded part is 239.4 sq ft.

User Azhar Bandri
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