Question

10. Three rectangles of dimensions 4 m x 3 m are removed from a large rectangle of
dimensions 10 m x 8 m. Find the area of the remaining part.
4
10​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that dimensions of a large rectangle are 10 m and 8 m, from the large rectangle 3 small rectangles are cut of dimensions 4 m and 3 m. We have to find the area of the remaining part.

At first we'll find the area of the large rectangle. After that, we'll find the area of the 3 small rectangles. Then we'll subtract the area of the 3 small rectangles from the area of large rectangle to find the area of remaining part.

Given:

• Three rectangles of dimensions 4 m x 3 m are removed from a large rectangle of dimensions 10 m x 8 m.

To calculate:

• Area of remaining part.

Calculation:

According to the question,

$\bigstar \: \boxed{\sf {Area_{(Remain)} = Area_{(Big \: rect.)} - Area_{(3 \: small \: rect.)} }}$

• rect. refers to rectangle.

$\underline{\small \sf {\maltese \; \; \; Finding \: area \: of \: big \: rectangle : \; \; \; }}$

Given Dimensions :

• Breadth of the large rectangle = 8 m
• Length of the large rectangle = 10 m

Area of large rectangle :

★ Area of rectangle = Length × Breadth

$\longrightarrow \sf {Area_{(Large \: rect.)} = 8 \: m \times 10 \: m }$

$\longrightarrow \sf \red {Area_{(Large \: rect.)} = 80 \: m^2 }$

$\underline{\small \sf {\maltese \; \; \; Finding \: the \: area \: of \: 3\: small \: rectangles : \; \; \; }}$

Given Dimensions :

• Length of each small rectangle = 4 m
• Breadth of each small rectangle = 3 m

Area of 1 small rectangle :

★ Area of rectangle = Length × Breadth

$\longrightarrow \sf {Area_{(smal \: rect.)} = 4 \: m \times 3 \: m }$

$\longrightarrow \sf {Area_{(small \: rect.)} = 12 \: m^2 }$

Area of 3 small rectangles :

★ Area of three small rectangles = 3 × Area of 1 small rectangle

$\longrightarrow \sf { Area_{(3 \: small \: rect.)} = (3 \times 12)\: m^2 }$

$\longrightarrow \sf \red{ Area_{(3 \: small \: rect.)} = 36 \: m^2 }$

Now, substitute the values in the formula given below to find out the required answer.

$\bigstar \: \boxed{\sf {Area_{(Remain)} = Area_{(Big \: rect.)} - Area_{(3 \: small \: rect.)} }}$

$\longrightarrow \sf {Area_{(Remain)} = 80 \: m^2 - 36 \: m^2 }$

$\longrightarrow \sf\red {Area_{(Remain)} = 44 \: m^2 }$

Therefore, the area of the remaining part is 44 m².

Answer 2

Given :

Dimensions of Bigger Rectangle :

• Length = 10m
• Breadth = 8m

Dimensions of Smaller Rectangle :

• Length = 4m
• Breadth = 3m

To Find :

• Area of the remaining part.

Solution :

✰ In this question, it is given that three rectangles of dimensions 4m × 3m are removed from from a larger rectangle of dimensions 10m × 8m and we have to find the area of the remaining part. So now we will find the area of the bigger and smaller rectangle separately and after that we will multiple the area of smaller rectangle by 3 as 3 smaller rectangles are removed from the bigger rectangle. After getting the area of 3 rectangles we will substract the area of those 3 rectangles from the area of the bigger rectangle to find the area of the remaining part.

⠀⠀⠀

Area of Bigger Rectangle :

⠀⠀⠀⟼⠀⠀⠀Area = Length × Breadth

⠀⠀⠀⟼⠀⠀⠀Area = 10 × 8

⠀⠀⠀⟼⠀⠀⠀Area = 80m²

⠀

Area of Smaller Rectangle :

⠀

⠀⠀⠀⟼⠀⠀⠀Area = Length × Breadth

⠀⠀⠀⟼⠀⠀⠀Area = 4 × 3

⠀⠀⠀⟼⠀⠀⠀Area = 12m²

⠀

Area of 3 Smaller Rectangles :

⠀⠀⠀⟼⠀⠀⠀Area = Smaller area × 3

⠀⠀⠀⟼⠀⠀⠀Area = 12 × 3

⠀⠀⠀⟼⠀⠀⠀Area = 36m²

⠀

Area of Remaining part :

⟼ Area = Bigger Area - Smaller Area

⟼ Area = 80 - 36

⟼ Area = 44m²

⠀

Thus Area of the Remaining part is 44m²

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