Answer

Verified

447.6k+ views

Hint: - Here we go through by first figure out the diagram what the question says then apply the formula of area of rectangle and the area of semicircle. And then add them together to find the total area of the door.

Complete step-by-step answer:

Here it is given that the width of the door is 4 on which the semicircular is surmounted. By the figure we can say that the length of the width is equal to the diameter of the semi-circle.

Hence the radius of the semicircle ‘r’ is $\dfrac{4}{2} = 2$ because the radius is half of the diameter.

Given width of door =4.

Length of door =10.25.

And the door is surmounted by a semicircle of radius =2.

First we find out the area of rectangular figure by the help of the formula of area of rectangle i.e. $l \times b$

Area of rectangular figure =$l \times b = 4 \times 10.25 = 41$sq. unit

Now we find out the area of semicircle that is surmounted on the rectangular part by the formula of area of semicircle i.e. $\dfrac{{\pi {r^2}}}{2}$

Area of semicircular figure=$\dfrac{{\pi {r^2}}}{2} = \dfrac{{22}}{7} \times \dfrac{1}{2} \times 2 \times 2 = 6.28$ sq. unit

Now for the total area of the door we add the area of the rectangular part with the area of the semicircular part. I.e. 41+6.28=47.28 sq. unit.

Note: - Whenever we face such a type of question the key concept for solving the question is first figure out the diagram then apply the formula of area to find out the area of the given figure. And always remember one thing in mind that the unit of area is always in the form of sq. unit here in this question no unit is given to the question so we simply write its unit as sq. unit to show that is the value of area.

Complete step-by-step answer:

Here it is given that the width of the door is 4 on which the semicircular is surmounted. By the figure we can say that the length of the width is equal to the diameter of the semi-circle.

Hence the radius of the semicircle ‘r’ is $\dfrac{4}{2} = 2$ because the radius is half of the diameter.

Given width of door =4.

Length of door =10.25.

And the door is surmounted by a semicircle of radius =2.

First we find out the area of rectangular figure by the help of the formula of area of rectangle i.e. $l \times b$

Area of rectangular figure =$l \times b = 4 \times 10.25 = 41$sq. unit

Now we find out the area of semicircle that is surmounted on the rectangular part by the formula of area of semicircle i.e. $\dfrac{{\pi {r^2}}}{2}$

Area of semicircular figure=$\dfrac{{\pi {r^2}}}{2} = \dfrac{{22}}{7} \times \dfrac{1}{2} \times 2 \times 2 = 6.28$ sq. unit

Now for the total area of the door we add the area of the rectangular part with the area of the semicircular part. I.e. 41+6.28=47.28 sq. unit.

Note: - Whenever we face such a type of question the key concept for solving the question is first figure out the diagram then apply the formula of area to find out the area of the given figure. And always remember one thing in mind that the unit of area is always in the form of sq. unit here in this question no unit is given to the question so we simply write its unit as sq. unit to show that is the value of area.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE