Question

In the following figure from a rectangular region ABCD with AB= 20 cm, a right triangle AED with AE= 9 cm and DE= 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (Take $(\pi=\frac{22}{7})$).​

Answer 1

Answer:

The Area of shaded region is 334.39 cm²

Step-by-step explanation:

Given :

Length of a rectangle (AB) = DC = 20 cm

Breadth of a rectangle( BC) = AD = 15 cm

AE  = 9 cm ,  ED = 12 cm

AREA OF RECTANGLE = length X breadth= 20 × 15 = 300 cm²

AREA OF RECTANGLE = 300 cm²

Diameter of Semicircle = Breadth of a rectangle = 15 cm

Radius of Semicircle = diameter/2 = 15 /2 cm

AREA OF SEMICIRCLE = ½ πr²

= ½ ×(22/7) × (15/2)²  

= (22 × 225) /(4 × 14)

= 4950/56  

= 88.39 cm²

Area of right angled ∆ = ½ × Base × height

AREA OF RIGHT ANGLED ∆AED = ½ × AE × ED

= ½ × 9 × 12  = 9 × 6

= 54 cm²

Area of shaded region = Area of rectangle - Area of right angled ∆AED  + Area of semicircle  

AREA OF SHADED REGION  = 300 - 54 + 88.31 = 246 + 88.39= 334.39 cm²

Hence, the Area of shaded region is 334.39 cm²

HOPE THIS ANSWER WILL HELP YOU….

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