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Published on: 02/08/2018
In Perimeter and Area contains important questions in CBSE 7th Standard Mathematics. It also covered with the most important questions in Perimeter and Area.
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1.
The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.
2.
The perimeter of a rectangular sheet is 100cm. If the length is 35 cm, find its breadth. Also, find the area.
3.
Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also, find its perimeter.
4.
The length and the breadth of a rectangular piece of land are 500 m and 300 m, respectively. Find the cost of the land, if 1m2 of the land costs Rs 10000.
5.
Give two examples, where the area does not increase when perimeter increases.
6.
Give two examples, where the area increases as the perimeter increases.
7.
Yogesh walks to school every day. His school is located 500 m from his house. What is the total distance walked by Yogesh every day?
8.
The dimensions of a lawn are in the ratio 4: 1 and its area is 2500 m2. What is the length of the lawn?
9.
The length of a rectangle is 1cm more than its breadth. The diagonal is 29 cm. Find the area of the rectangle.
10.
One side of a rectangular lawn is 12 m and its diagonal is 13 m. Find the area of the field.
11.
Find the area of a square, whose each side is 2.5 cm. Also, find the perimeter.
12.
Find the area of a rectangle, which is 30 cm long and 25 cm broad.
13.
What will be the area of the largest square that can be cut out of a circle of radius 10 cm?
100 cm2
200 cm2
300 cm2
400 cm2
14.
If radius of a circle is increased to twice its original length, how much will the area of the circle increase?
1.4 times
2 times
3 times
4 times
15.
If the sides of a parallelogram are increased to twice of its original lengths, how much will the perimeter of the new parallelogram?
1.5 times
2 times
3 times
4 times
16.
A cow is tied with a rope of 7 m. The grass grazed field by the cow is
144 m2
140 m2
154 m2
164 m2
17.
The radii of two concentric circles are 7 m and 9 m. The area enclosed between them is
90 m2
90.47 m2
100 m2
100.48 m2
18.
A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle. Then the Area of the circle is
196 cm2
212 cm2
616 cm2
644 cm2
19.
A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is
22 cm
14 cm
11 cm
7 cm
20.
Find the length of a parallelogram, whose area is 246 cm2 and base is 20 cm2.
123 cm
13.2 cm
12.3 cm
1.32 cm
21.
Find the area of a square park, whose perimeter is 96 cm.
576 cm2
626 cm2
726 cm2
748 cm2
22.
The breadth of a rectangle whose length is 12 cm and perimeter is 36 cm is
6 cm
3 cm
9 cm
12 cm
23.
A square park has each side 50 cm. At each corner of the park, there is a flower bed in the form of a circle whose radius 7 m, as shown in the figure, find the area of remaining part of two park.
24.
Area of a rectangular field is 3584 cm2 and the length and the breadth are in the ratio 7: 2, respectively. What is the perimeter of the rectangle?
1.
Let b be the breadth of the rectangular park.
Given, side of a square park, a = 60 m and length of the rectangular park, I = 90 m
Now, area of a square park = (Side)2 = (60)2 = 3600 m2
According to the question,
Area of a rectangular park = Area of a square park
\(\Rightarrow\) I x b = 3600 [\(\therefore\) area of a rectangular park = I x b]
\(\Rightarrow\) 90 x b = 3600 \(\Rightarrow\) b = \(\frac{3600}{90}\Rightarrow\) b = 40 m
Hence, the breadth of a rectangular park is 40 m.
2.
Given, perimeter of a rectangular sheet = 100 cm and length of a rectangular sheet, I = 35 cm
Let b be the breadth of a rectangular sheet .
We know that, perimeter of a rectangular sheet = 2 (/ + b)
\(\Rightarrow\) 2(/ + b) = 100 \(\Rightarrow\) 2(35 + b) = 100
\(\Rightarrow\) \(35+b=\frac{100}{2}\) [dividing by 2 on both sides]
\(\Rightarrow\) 35 + b = 50 \(\Rightarrow\) b = 50 - 35 \(\Rightarrow\) b = 15 cm
\(\therefore\) Area of a rectangular sheet = I X b = 35 x 15 = 525 cm2
Hence, the breadth and area of a rectangular sheet are 15 cm and 525 cm2, respectively.
3.
Let b be the breadth of a rectangular plot of land.
Given, length of a rectangular plot of land, I = 22 m and area of a rectangular plot of land = 440 m2
We know that area of a rectangular plot of land = I x b
\(\Rightarrow\) 440 = 22 X b \(\Rightarrow\) 22b = 440 \(\Rightarrow\) b = \(\frac{440}{22}\) = 20 m
\(\therefore\) Perimeter of a rectangular plot of land = 2(/ + b)
= 2(22 + 20) = 2 x 42 = 84 m
Hence, the breadth and perimeter of a rectangular plot of land are 20 m and 84 m, respectively.
4.
Given, length of a rectangular piece of land, I = 500 m and breadth of a rectangular piece of land, b = 300 m
Cost of 1m2 land = Rs 10000
\(\therefore\) Cost of 150000 m2 land = Rs 10000 x 150000
= Rs 1500000000
Hence, the cost of 150000 m2 land at the rate of 10000 per m2 is Rs 1500000000.
5.
There are two example given below:
Example 1. Let length of a rectangle = 4 cm and breadth of a rectangle = 3 cm
\(\therefore\) Area of a rectangle = I X b = 4 X 3 = 12 cm2
and perimeter of a rectangle = 2(1 + b)
= 2 (4 + 3) = 2 x 7 =.14cm
Again, let the length of a rectangle = 6 cm and breadth of a rectangle = 2 cm
\(\therefore\) Areaofarectangle = l x b = 6 x 2 = 12cm2
and perimeter of a rectangle = 2(1 + b) = 2(6 + 2)
= 2 X 8=16 cm
Hence, perimeter of rectangles increase, but area of both rectangles are same.
Example 2. Let length of a rectangle = 4 cm and breadth of a rectangle = 3 cm
\(\therefore\) Area of a rectangle = I X b = 4 X 3 = 12 cm2
and perimeter of a rectangle = 2(1 + b) = 2 (4 + 3)
= 2 X 7=14 cm
Again, let the length of a rectangle = 12 cm and breadth of a rectangle = 1cm
\(\therefore\) Area of a rectangle = I X b = 12 x 1= 12 cm2
and perimeter of a rectangle = 2(1 + b) = 2(12 + 1)
= 2 x 13= 26 cm
Hence, perimeter of rectangle increases, but area of both rectangles are same.
6.
There are two examples as given below:
Example 1. Let the length of a rectangle = 5 cm and breadth of a rectangle = 3 cm
\(\therefore\) Area of a rectangle = Length X Breadth
= 5 X 3=15 cm2
and perimeter of a rectangle = 2 (Length + Breadth)
= 2 ( 5 + 3) = 2 X 8 = 16 cm
Again, let the length of a rectangle = 6 cm and breadth of a rectangle = 5 cm
\(\therefore\) Area of a rectangle = Length X Breadth = 6 X 5 = 30 cm2
and perimeter of a rectangle = 2 (Length + Breadth)
= 2 (6 + 5) = 2 X 11 = 22 cm
Thus, for both rectangles, area increases as the perimeter Increases.
Example 2. Let the side of a square = 4 ern
\(\therefore\) Perimeter of square = 4 X Side = 4 x 4 = 16 cm
and area of square = (Side X Side)
= 4 X 4 = 16 sq ern
Again, let the side of a square = 5 cm
\(\therefore\) Perimeter of square = 4 X Side = 4 x 5 = 20 cm
and area of square = Side X Side
= 5 x 5 = 25 sq cm
Thus, for both squares, area increases as the perimeter Increases.
7.
500 m.
8.
100 m.
9.
420 cm2
10.
60 m2
11.
6.25 cm2, 10 cm
12.
750 cm2
13.
(b)
200 cm2
14.
(d)
4 times
15.
(b)
2 times
16.
(c)
154 m2
17.
(d)
100.48 m2
18.
(c)
616 cm2
19.
(b)
14 cm
20.
(c)
12.3 cm
21.
(a)
576 cm2
22.
(a)
6 cm
23.
2346 m2
24.
288 cm
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