Unit-6: Mensuration
(a) Heron's formula
(b) Pyramids
Q1.
In heron's formula 's' is _________.
(a) radius (b) diameter (c) semi-perimeter (d) center
Solution.
(c) semi-perimeter
Solution
Q2.
Two sides of a triangle is 10 cm, 12 cm and its semi-perimeter is 18 cm. find the third side.
(a) 15 cm (b) 14 cm (c) 12 cm (d) 10 cm
Solution.
(b) 14 cm
Solution
Q3.
Find the height of isosceles triangle, if a = 5, b = 3 {(a = equal side),(b = base)}.
(a) √91/4
(b) √91 (c) 91/4 (d) √20
Solution.
(a) √91/4
Height of triangle = (√a2 - b2/4)
Solution
Q4.
Find the length of equal side whose one side is 20 cm longer than each of its equal sides and semi-perimeter is 100 cm.
(a) 20 (b) 40 (c) 60 (d) 80
Solution.
s = 100
25 = 200
x + x + x + 20 = 200
3x = 180
x = 60
(x is length of equal side.)
Solution
Q5.
Semi-perimeter is 450 cm and its sides are in the ratio 6:10:8, find the area of this triangular park (in cm2).
(a) 18450 cm2 (b) 33750 cm2 (c) 16200 cm2 (d) None of these
Solution.
(b) 33750 cm2
Solution
Q6.
In a right-angled triangle sum of two perpendicular sides is 7 cm and sum of square of these perpendicular side is 25.The area of triangle is __________ cm2 .
(a) 8 cm2 (b) 12 cm2 (c) 4 cm2 (d) 6 cm2
Solution.
x + y = 7
x 2 + y 2 = 25
(x + y)2 = x2 + y2 + 2xy
49 = 25 + 2xy
2xy = 24
xy = 12
Area of triangle = 1/2xy = 6 cm2
Solution
Q7.
If each side of the triangle is doubled , then area of triangle will increase ___________ percentage.
(a) 300 (b) 400 (c) 200 (d) 100
Solution.
(a) 300
Solution
Q8.
Heron's formula is .
(a) √s(s-a)(s-b)(s-c) (b) 1/2 Base x Heeight (c) (√3)/4 a2 None of these(d)
Solution.
(a) √s(s-a)(s-b)(s-c)
Solution
Q9.
Base area 60m2 and height is 10 m. find the volume of pyramid.
(a) 200 m3
(b) 100 m3 (c) 50 m3 (d) 280 m3
Solution.
(a) 200 m3
Solution
Q10.
In a figure sum of vertices and faces are 20, Number of edges will be ____________.
(a) 20 (b) 18 (c) 16 (d) 14
Solution.
(b) 18
Euler's relation
Vertices + Faces = edges + 2
Solution
