Question

b. find the area of the shaded region. write your solutions and answers on a separate sheet of paper. use π = 3.14

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Answer 1

Given :

Given a rectangle with breadth and length as 16cm and 10cm along with two semicircles having their diameter 10cm which is the length of the rectangle.

To find :

We have to find the area of the shaded region.

Explaination :

Here, we are given a rectangle whose length is same as the diameter of the semicircles in it. Now, we'll find the area of the shaded region by first knowing the area of two semicircles and then subtracting this value from the area of the rectangle.

Solution :

In the rectangle :

• Length = 10cm
• Breadth = 16cm

Area of rectangle = Length (Breadth)

• Area = 10cm(16cm)
• Area = 160cm²

For the semicircle :

• Diameter = 10cm
• Radius = 5cm

Area of semircircle = πr²/2

• Area = 3.14(5cm)²/2
• Area = 3.14(25cm²)/2
• Area = 78.5cm²/2
• Area = 39.25cm²

Area of 2 semircircles = 2(πr²/2)

• Area of semircircles = 2(39.25cm²)
• Area of semircircles = 78.5cm²

Area of shaded region = Area of rectangle - Area of semircircles

• Area = 160cm² - 78.5cm²
• Area = 81.5cm²

Therefore, the area of the shaded region is 81.5cm².

Answer 2

Given :

Given a rectangle with breadth and length as 16cm and 10cm along with two semicircles having their diameter 10cm which is the length of the rectangle.

To find :

We have to find the area of the shaded region.

Explaination :

Here, we are given a rectangle whose length is same as the diameter of the semicircles in it. Now, we'll find the area of the shaded region by first knowing the area of two semicircles and then subtracting this value from the area of the rectangle.

Solution :

In the rectangle :

Length = 10cm

Breadth = 16cm

Area of rectangle = Length (Breadth)

Area = 10cm(16cm)

Area = 160cm²

For the semicircle :

Diameter = 10cm

Radius = 5cm

Area of semircircle = πr²/2

Area = 3.14(5cm)²/2

Area = 3.14(25cm²)/2

Area = 78.5cm²/2

Area = 39.25cm²

Area of 2 semircircles = 2(πr²/2)

Area of semircircles = 2(39.25cm²)

Area of semircircles = 78.5cm²

Area of shaded region = Area of rectangle - Area of semircircles

Area = 160cm² - 78.5cm²

Area = 81.5cm²

Therefore, the area of the shaded region is 81.5cm².

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