7th Grade > Mathematics
AREA AND PERIMETER MCQs
Perimeter And Area
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Steps: 2 Marks
Answer: 1 Mark
Given side of a square = 8 cm
If it is cut into two equal parts the along the length, then:
the rectangles formed will have the length and breadth as 8 m and 4 m respectively
The perimeter of the rectangle will be 2×(8+4) = 24m
The perimeter of the rectangle will be equal to the circumference of the circle.
The circumference of the circle whose radius is R m = 2πR
2πR = 24
R = 12πm
R = 3.81 m
The radius of the circle is 3.81 m.
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Formula: 1 Mark
Steps: 1 Mark
Application: 1 Mark
Answer: 1 Mark
Given that
Area of a parallelogram=48 cm2
The parallelogram is divided into two congruent triangles.
Area of parallelogram = 2(Area of triangle)
Area of triangle = 48 cm22=24cm2
Area of triangle = 12×base×height
24 cm2=12×base×4cm
base = 12 cm
So, measure of base of the triangle is 12 cm.
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Formula: 2 Marks
Answer: 1 Mark
Let the side of given square be A cm
Area of the given square = A2
Radius of the given circle = A2 cm
Area of the circle = (π)(A2)2
= π4×(A2)
= 0.785A2
A2>0.785A2
So square has more area compared with circle
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Steps: 2 Marks
Answer: 1 Mark
Given that
The length of each side of a square = 4 m
Area of the given square = (4)2
= 16m2
As per the question, the ratio of length and breadth of the rectangle is 2
Area of the rectangle is given = 16 m2
The area of the rectangle whose length is L m and breadth is B m is L × B m2
L = 2B ( as per question)
2B × B = 16
B = 2 × √2m
So, L = 2(2 × √2m)
= 4 ×√2m
So, the length of the rectangle is 4 ×√2m.
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Formula: 1 Mark
Application: 2 Marks
Answer: 1 Mark
Given that
A square of side 'x' meters is bent into a circle.
The perimeter of the square = 4×x
The circle will have the same perimeter as that of the square = 4×x metres
Circle will be having a radius(r) = 4x2π
Area of the Circle so formed
= π×(4x2π)4x2πm2=4x2π
The circle which is half cut has a circumference of 2x.
Square bent from half circle has the circumference of 2x meters.
Side of the square = 2x4
Area of the square = x24
Putting x = 2
We get the area of the circle
= 4π×22 = 5.09 m2
The area of the square = 44 = 1m2
The difference between the area of the circle and the area of the square
= 5.09 - 1 = 4.09 m2
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Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
According to the question, if base = 12 cm and height = 5 cm
So, area = base × height = 12 × 5 = 60 cm2
Now, if base = 8 cm and now we know that area of a parallelogram is 60 cm2
So, Distance between 8 cm sides = 608 = 7.5 cm
So, the distance between the 8 cm sides is 7.5 cm.
Given two squares of the same length. One square has a triangle in it with its vertices coinciding with three vertices of the square. The other square contains a circle touching all mid points of the sides of the square.Which of these two will have a greater area and what is the difference in the areas if the length of the given square is 4m?
[4 MARKS]
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Steps: 3 Marks
Answer: 1 Mark
The given square has a length of 4 m
Area of the Triangle = 0.5 × 4 × 4 = 8 m2
The radius inscribed within the square has radius of 42=2m
Area of the given circle = π × 22 =12.56 m2
Circle has a greater area compared to triangle.
Difference between the area of the circle and triangle = 4.56 m2
A man runs in a circular path. He runs towards the center from the circumference and after reaching the center he suddenly changes his direction from his original path at 180 degrees to the original direction and stopped when he reached the circumference. Find the area and perimeter of the circle, given that, the man ran 8 meters in the above-described path? [4 MARKS]
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Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark
Given that
Total distance travelled by the man = 8 m
The man reached toward the center from the circumference to center and back to the center from the circumference.
So, the total distance covered by him is equal to twice the radius of the circle.
Let 'r' be the radius of the circle.
So, 2r = 8, r = 4
We know that area of the cicle is given by, Area=π×(r)2m2
Area of the given circle =π×(4)2m2
= (3.14)×(16)m2
=50.24m2
The perimeter of a circle= 2×π×r
=2×π×4
=25.14 m
So, the area of the given circle is 50.24m2, and the perimeter is 25.14 m.