Question

The shape of a rectangle is semi-circle at the both ends . The length of the rectangle is 30 m and the radius of the semi-circle is 7m , then find its area and perimeter​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Question:-

The shape of a rectangle is semi-circle at the both ends . The length of the rectangle is 30 m and the radius of the semi-circle is 7m ,then find its area and perimeter

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Given:-

The shape of a rectangle is semi-circle at the both ends . The length of the rectangle is 30 m and the radius of the semi-circle is 7m

To find:-

Area and perimeter of semicircle and rectangle and area, perimeter of full rectangle

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Solution:-

According to the question:-

Length of rectangle=30m

Radius of semicircle =7m

Length of rectangle=30m-(7m) =23m

So,

breadth of rectangle=7m

First we need to find area of rectangle and two semicircles and add that so we get the area of full rectangle

As we know,

Area of rectangle=length×breadth

On putting values we get,

=23m×7m

$= 161 {m}^{2}$

Next, area of semicircles

Measures of both semicircles are equal

So, we need to find two times

As we know,

Area of semicircle=

$\pi \: {r}^{2}$

r=radius

Taking π=22/7

On putting values we get,

$\frac{22}{7} \times {7}^{2} m$

$= \frac{22}{7} \times 49 {m}^{2}$

On cancelling with seven we get,

$= \frac{22}{1} \times 7 {m}^{2}$

$= 154 {m}^{2}$

Second semicircle also same in measure so we need to multiply by 2 of first semicircle's area

=154m^2×2

=308m^2

This is additionally I have provided information:-

Area of full rectangle=Area of rectangle+area of two semicircles

On putting values we get,

$= 161 {m}^{2} + 308 {m}^{2}$

$= 469 {m}^{2}$

Therefore area of full rectangle=469m^2

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Second we need to find perimeter of rectangle and perimeter of two semicircles and add that so we can find the perimeter of full rectangle

As we know

Perimeter of rectangle=2(length+breadth)

On putting values we get,

=2(23m+7m)

=2(30m)

=60m

Perimeter of rectangle=60m

Next, we have to find perimeter of two semicircles

As we know,

Perimeter of

Perimeter of semi circle=

$\frac{2\pi \: r}{2} + d$

Or,

$\pi \: r + d$

As because when two in the numerator and denominator are cancelled

We don't know the diameter

So we have to multiply the radius by 2 (always radius in a circle or semicircle multiplied by 2 we can get the diameter of the circle or semicircle)

=7m×2

=14m

Diameter of semicircle is 14m

By using formula(taking π=22/7)

$= \frac{22}{7} \times 7m + 14m$

On cancelling with 7 we get

$= \frac{22}{1} \times 1m + 14m$

$= 22m + 14m$

=36m

Next,

Perimeter of full rectangle=perimeter of rectangle+perimeter of semicircle

on putting values we get,

=60+36m

=96m

Answer: Area of full rectangle is 469m^2 and perimeter of full rectangle is 96m

Step-by-step explanation:

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