Question

In the given figure, ABCD is a trapezium with AB || DC with AB = 16 cm, DC = 24 cm and distance between parallel sides is 15 cm. Four circles of equal radii 3.5 cm with centres at A, B, C and D have been drawn. Find the area of the shaded region.
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Answer 1

Area of Shaded Region is 415.395 cm².

Step-by-step explanation:

Given:

ABCD is a trapezium

AB || DC

AB = 16 cm, DC = 24 cm and Height = 15 cm

Radius = 3.5 cm

To Find:

Area of the shaded region = ?

Solution:

First we will have Area of Trapezium

$\textrm{Area of Trapezium}=0.5\textrm{Sum of Parallel Sides}\times Height$

Substituting the values we get

$\textrm{Area of Trapezium}=0.5(16+24)\times 15=300\ cm^{2}$

Now Area of Circle,

$\textrm{Area of Circle}=\pi(radius)^{2}$

Substituting the values we get

$\textrm{Area of Circle}=3.14\times 3.5^{2}=38.465\ cm^{2}$

Now for Shaded Region

All the four corners will make one full circle therefore,

$\textrm{Area of Shaded Region}=\textrm{Area of Trapezium}+3\times \textrm{Area of Circle}$

Therefore we have,

$\textrm{Area of Shaded Region}=300+3\times 38.465=415.395\ cm^{2}$

Area of Shaded Region is 415.395 cm².