Question

the perimeter and the area of the shaded region in the following figure all the measurements are in centimetre​

Answer 1

Given :-

• Here, we have figure maded by joining semicircle and rectangle.

• Length of rectangle is 10.5 units and it's width is 4 units.

To Find :-

• Perimeter and area of figure.

Solution :-

Firstly, finding perimeter of the figure :-

• Diameter (D) of semicircle = 10.5 – 3.5

[ Because whole length is 10.5 units and length upto first end of diameter is 3.5 units. So, we will subtract 3.5 from 10.5, to get diameter of semicircle ]

➱ㅤㅤㅤD = 10.5 – 3.5

➱ㅤㅤㅤD = 7

∴ Diameter of semicircle is 7 units

So, it's radius = 7/2 units

❂ [Perimeter of semicircle = πr] ❂

Putting all values :-

➱ㅤㅤㅤ22/7 × 7/2

➱ㅤㅤㅤ(22 × 7)/(7 × 2)

➱ㅤㅤㅤ22/2

➱ㅤㅤㅤ[ 11 ] ★

∴ Perimeter of semicircle is 11 units

But we need measure of only curved side

So, we will subtract it's diameter from perimeter

➱ㅤㅤㅤ11 – 7

➱ㅤㅤㅤ[ 4 ] ★ㅤㅤㅤ– – – – – – [1]

Now,

[Perimeter of rectangle = Sum of all sides]

But here we need measure upto ends of diameter only, therefore we will subtract 7 from it's perimeter.

Putting all values :-

➱ㅤㅤㅤ10.5 + 4 + 10.5 + 4 – 7

➱ㅤㅤㅤ29 – 7

➱ㅤㅤㅤ[ 22 ] ★ㅤㅤㅤ– – – – – – [2]

★ To get perimeter of whole figure we will add [1] and [2] :-

➱ㅤㅤㅤ4 + 22

➱ㅤㅤㅤ[ 26 ] ★

∴ Perimeter of given figure is 26 units

Now, finding it's area :-

[It's area = area of rectangle + area of semicircle]

✴ Solving :-

➱ㅤㅤ[ l × w ] + [ πr² ÷ 2 ]

➱ㅤㅤ[10.5 × 4] + [(22/7 × 7/2 × 7/2) ÷ 2]

➱ㅤㅤ42 + (38.5 ÷ 2)

➱ㅤㅤ42 + 19.25

➱ㅤㅤ[ 61.25 ] ★

∴ Area of given figure = 61.25 sq.units

• Perimeter of fig = 26 units

• Area of fig = 61.25 sq.units

ㅤㅤㅤ✴ Hence Solved ✴

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

Hope this attachment helps you.