1. If the length of the diagonal of a square is 7.4 cm, then the area of the square is:
a) 25.38 cm²
b) 27.38 cm²
c) 30.38 cm²
d) 34.38 cm²
2. The length of the diagonal of a square is 6a cm. The area of the square is:
a) 18a²
b) 36a²
c) 72a²
d) 12a²
3. The diagonal of a square is 6√2 cm. The diagonal of another square whose area is three times that of the first square is:
a) 6√2 cm
b) 9 cm
c) 6√3 cm
d) 12 cm
4. The side of a square P is (x + y) cm. The side of another square whose area is three times the area of square P is:
a) (x+y)
b) √3(x+y)
c) 3(x+y)
d) (x+y)√9
5. The difference of the areas of two squares drawn on two line segments is 48 sq. cm. If the length of one line segment is 4 cm more than the other, find the length of the greater line segment.
a) 8 cm
b) 12 cm
c) 14 cm
d) 16 cm
6. If the sides of two squares are in the ratio 3 : 7, then the ratio of their areas is:
a) 3 : 7
b) 7 : 3
c) 9 : 49
d) 21 : 49
7. The ratio of the area of a square to the area of the square drawn on half of its diagonal is:
a) 2 : 1
b) 1 : 2
c) 4 : 1
d) 1 : 4
8. From the four corners of a square sheet of side 6 cm, four pieces, each in the shape of a quarter circle of radius 3 cm, are cut out. What is the area of the remaining portion?
a) 36 − 9π cm²
b) 36 − 18π cm²
c) 36 − 9π/2 cm²
d) 18 − 9π cm²
9. A rectangle has sides 8 cm and 6 cm. Find the ratio of the area of the rectangle to the area of the square drawn on its diagonal.
a) 12 : 25
b) 25 : 12
c) 6 : 25
d) 25 : 6
10. From the four corners of a square sheet of side 14 cm, four pieces each in the shape of a quarter circle of radius 7 cm are cut out. What is the area of the remaining portion? (π = 22/7)
a) 42 cm²
b) 44 cm²
c) 46 cm²
d) 48 cm²
1. The perimeters of two squares are 16 cm and 20 cm. The perimeter (in cm) of a third square whose area is equal to the sum of the areas of these two squares is:
a) 4√41
b) 8√41
c) 16√41
d) 20√41
2. The perimeters of two squares are 52 cm and 20 cm. The perimeter (in cm) of a third square whose area is equal to the difference of the areas of the two squares is:
a) 24 cm
b) 12 cm
c) 40 cm
d) 48 cm
3. If the ratio of the areas of two squares is 144 : 196, then the ratio of their perimeters is:
a) 12 : 14
b) 6 : 7
c) 144 : 196
d) 24 : 28
4. The perimeters of two squares are 36 cm and 20 cm. The perimeter (in cm) of a third square whose area is equal to the difference of the areas of these two squares is:
a) 16
b) 20
c) 24
d) 28
5. A garden is divided into two square plots with perimeters 24 m and 32 m. A third square plot has an area equal to the sum of the areas of these two plots. Find the perimeter of the third plot.
a) 36 m
b) 38 m
c) 40 m
d) 42 m
6. Two square tiles have perimeters 60 cm and 36 cm. A third square tile has area equal to the difference of areas of these two tiles. Find the perimeter of the third tile.
a) 40 cm
b) 44 cm
c) 48 cm
d) 52 cm
7. The areas of two square fields are in the ratio 225 : 625. Find the ratio of their perimeters.
a) 2 : 3
b) 3 : 4
c) 3 : 5
d) 4 : 5
8. Two square parks have perimeters 40 m and 24 m. A third square park has area equal to the difference of the areas of the two parks. Find the perimeter of the third park.
a) 28 m
b) 30 m
c) 32 m
d) 34 m
9. Two square shaped farms have perimeters 68 m and 60 m. A third square farm has area equal to the difference of the two farms. Find its perimeter.
a) 28 m
b) 30 m
c) 32 m
d) 34 m
10. Two square playgrounds have perimeters 48 m and 36 m. A third square playground has area equal to the sum of the areas of the two playgrounds. Find its perimeter.
a) 55 m
b) 58 m
c) 60 m
d) 64 m
11. The areas of two square rooms are in the ratio 441 : 576. A builder claims the ratio of their perimeters is 3:4. Is he correct? Find the actual ratio.
a) 5 : 6
b) 6 : 7
c) 7 : 8
d) 8 : 9
12. Two square plots have perimeters 48 m and 20 m. A third square plot has area equal to the sum of areas of both plots. Find the perimeter of the third plot.
a) 48 m
b) 50 m
c) 52 m
d) 54 m
1. How many tiles, each of area 9 decimeter², are required to cover a rectangular floor 6 m long and 4.5 m broad?
a) 250
b) 300
c) 350
d) 400
2. If each side of a square is increased by 50%, then the increase in its area is:
a) 100%
b) 125%
c) 150%
d) 175%
3. The ratio of the area of the in-circle to the area of the circum-circle of a square is:
a) 1 : 4
b) 1 : 2
c) 2 : 1
d) 1 : √2
4. The sides of a right-angled triangle are 9 cm, 12 cm, and 15 cm. The area of the greatest square that can be inscribed in the triangle is:
a) 36 cm²
b) 49 cm²
c) 81 cm²
d) 64 cm²
5. The length of the rectangle is 4 cm more than the side of the square, and the breadth is 2 cm less than the side of the square. The perimeter of the rectangle is:
a) 28 cm
b) 32 cm
c) 36 cm
d) 40 cm
6. If the area of a triangle with base 10 cm is equal to the area of a square with side 10 cm, then the altitude of the triangle is:
a) 15 cm
b) 18 cm
c) 20 cm
d) 25 cm
7. An equilateral triangle is constructed on the side of a square. The ratio of the area of the triangle to the area of the square is:
a) √3 : 2
b) √3 : 4
c) 2 : √3
d) 1 : √3
8. If the perimeters of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 2 : 3, then the ratio of the area of the rectangle to that of the square is:
a) 12 : 25
b) 24 : 25
c) 16 : 25
d) 18 : 25
9. If the side of a square is decreased by 20%, then its area is decreased by:
a) 36%
b) 40%
c) 44%
d) 48%
10. One side of a rectangle is increased by 25%. To keep the area unchanged, the other side must be decreased by:
a) 20%
b) 25%
c) 30%
d) 33⅓%
11. A square is circumscribed about a circle of radius r. The area of the square lying outside the circle is:
a) 4r² − πr²
b) (4 − π)r²
c) (π − 4)r²
d) 2r²(π − 2)
12. A rectangular hall 12 m 60 cm long and 9 m 45 cm broad is to be paved with equal square tiles of the largest possible size. How many such tiles will be required?
a) 12
b) 60
c) 72
d) 84
13. The perimeters of two squares are in the ratio 5 : 9. What is the ratio of their areas?
a) 25 : 81
b) 5 : 9
c) 10 : 18
d) 125 : 729
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level – II |
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level – III |
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