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Find the area of the shaded region. Round to the nearest tenth where necessary (1 decimal places).

A=
14 in
8 in
5 in
25 in

Find the area of the shaded region. Round to the nearest tenth where necessary (1 decimal-example-1

1 Answer

6 votes

Answer:

5 in

Explanation:

The area of a composite shape: area of the bigger shape - the area of the smaller shape.

In this case, the bigger shape is the shaded region, and the smaller shape is the unshaded region.

1) Shaded region (bigger shape): 2(area of a trapezium) + area of the rectangle.

Area of a trapezium: 1/2 x (a + b) x h, where a and b are parallel lines and h is the height. We have to times the answer by 2 because there are two trapeziums in the shaded region.

Area of a rectangle: l x w, where l is the length and w is the width.

Trapeziums

= 1/2 x (3 + 8) x 5.5 x 2

= 1/2 x 11 x 5.5 x 2

= 1/2 x 60.5 x 2

= 30.25 x 2

= 60.5

Rectangle

= 14 x 3

= 42

Area of the shaded region (bigger shape): trapezium + rectangle

= 60.5 + 42

= 102.5

2) Unshaded region (smaller shape):

Area of a trapezium: 1/2 x (a + b) x h, where a and be are the parallel lines.

= 1/2 x (14 + 25) x 5

= 1/2 x 39 x 5

= 1/2 x 195

= 97.5

3) Area of the bigger shape - the area of the smaller shape

= 102.5 - 97.5

= 5 in²

User Touseef Murtaza
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