1.The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(a) 25
(b) 35
(a) 49
(d) 70
2.The base and altitude of a parallelogram are 12 cm and8 cm respectively. What is its area?
(a) 192
(b) 48
(c) 36
(d) 96
3.The perimeter of a rhombus PQRS is 68 cm. If the length of the diagonal PR is 30 cm, what will the length of the other diagonal QS be?
(a) 16 cm
(b) 8 cm
(c) 24 cm
(d) 32 cm
4.Two adjacent sides of a rectangle are in the ratio 3 : 11. If its area is 132 square metres, then what is its perimeter?
(a) 28 m
(b) 56 m
(c) 112 m
(d) 14 m
5.If each of any two opposite sides of a square is increased by one cm and each of the other two sides is decreased by one cm, we obtain a rectangle whose area is 63 cm2. What is the perimeter of the original square?
(a) 36 cm
(b) 32 cm
(c) 28 cm
(d) 44 cm
6.What is the area of a regular hexagon whose side measures 4 cm?
(a) 12 √3 (cm)^2
(b) 18√3 (cm)^2
(c) 24√3 (cm)^2
(d) 36√3 (cm)^2
7.A wire in the form of a circle of radius 3 .5 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(a) 60 cm^2
(b) 30 cm^2
(a) 45 cm^2
(d) 120 cm^2
8.A cow is tied to one corner of a closed shed located in a field. The dimensions of the shed are 15 m * 12 m and the length of the rope that is used to tie the cow is 10m. What is the area in which the cow can graze?
(a) 25 π m^2
(b) 50π m^2
(c) 75 π m^2
(d) 100π m^2
9.The base of a solid right prism is a right angled triangle whose hypotenuse and a side are 25 cm and 7 cm respectively. The height of the prism is 5 cm. What is the total surface area of the prism?
(a) 168 cm^2
(b) 280 cm^2
(a) 448 cm^2
(d) 508 cm^2
10.The lengths, breadths and volumes of two cuboid are in the ratio of 4: 5, 3 : 4 and 2 : 3, respectively. What is the ratio of their heights?
(a) 3 : 5
(b) 8 : 15
(c) 2 : 3
(d) 10 : 9
Answers .....
1.(b)
Area of a triangle = r * s
Where r is the in radius and s is the semi perimeter of the triangle
Area of triangle = 2.5 * 28/2 = 35
2.(d)
Area of a parallelogram
= base * altitude = 12 * 8 = 96
3.PQRS is a rhombus
If s is the side, 4s = 68
s = 68/4 = 17 cm‘
Let the centre of the rhombus be 0.
OR= 30/2 =15,RS=17,
RS2 = OR2+ OS2 gives
OS2= 172 152=64, OS = 8 cm
The other diagonal QS = 2 * 8 = 16 cm
4.(b)
Let 3x, 11x be the sides of the rectangle.
Area = 3x *11x = 33x2 = 132
X = 2
B = 3 * 2 = 6m, 1 = 11 * 2 = 22m
Perimeter= 2(22 + 6) = 56 cm
5.(b)
Let x be the side of the square.
Area of the rectangle = (x + 1) (x – 1) = 63
x2 – 1 = 63
x2 = 63 + 1 = 64
x = 8cm
Perimeter of the original square
= 4 * 8 = 32 cm
6.(c)
The hexagon can be divided into six equilateral triangles of equal areas.
Area of the hexagon = 6 × √3/4 ×4 ×4= 24√3
7.(b)
The circumference of the circle is equal to the perimeter of the rectangle.
Let l = 6x and b = 5x
2(6x + 5x) = 2 * 22/7 * 3.5 = x = 1
L = 6 cm and b = 5 cm
Area of the rectangle = 6 * 5 = 30
8.(c)
The area that can be grazed by the cow is in the form of three quadrants.
Total area that can be grazed
= ¾ × π(10)^2 75p m^2
9.(c)
The base of the prism is ABC
Where BC = 25 cm and AB = 7 cm
AC2 = BC2 – AB2 = 252 – 72 = 576
AC = √576 24 cm
Area of base = ½ * 24 * 7 = 84 cm2
Total surface area = (25 + 7 + 24) 5 + 2(84)
= 56 (5) + 168 = 448 cm2
10.(d)
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