# Mensuration – Exercise 4.6.4 – Class IX

1. Find the LSA and TSA of the following pyramid.

a) Square based pyramid with base 6 cm. and slant height 14 cm.

b) Triangular based pyramid with base 12cm, slant height 20 cm.

Solution:

1. a) Square based pyramid with base 6 cm. and slant height 14 cm.

A = 6;  L = 14

LSA = 1/2 pL

L  = 1/2 x  4axL

= 1/2 x 4 x 6 x 14 = 168m2

TSA = B + LSA = B + 1/2 p

= a2 + 168 = 62 + 168 = 36 + 168 = 204 cm2

(b) Triangular based pyramid with base 12cm, slant height 20 cm.

LSA = 1/2 pxL

L = 1/2 x 3 x axL = 1/2 x 3 x 12 x 20 = 3 x 12 x 10 = 360cm2

TSA = B + 1/2 p = √3/4 x 12 x 12 + 360

= 36√3 + 360

= 36(√3+10) cm2

1. Find the difference between the lateral and TSA of a square based pyramid with side 2.5 cm and slant height 8 cm.

Solution:

LSA = ?

TSA = ?

a = 2.5cm

L = 8cm

LSA = 1/2 PL

L = 1/2 x 4axL =1/2 x 4 x 2.5 x 8

=1/2 x 4 x 2.5 x 8

L= 40 cm2

TSA = B + LSA = B + 1/2 P

= a2 + 40

= (2.5)2 + 40

= 46.25cm2

Difference between TSA and LSA = TSA – LSA

=46.25 – 40 = 6.25cm2

1. Find the perimeter of a triangular based pyramid with slant height 18 m. and LSA = 360 m2

Solution:

LSA = 1/2 pL

L =  1/2 x p x L

360 = 1/2 x p x 18

p = 360×2/18 = 40m

1. The base and height of a square based pyramid is 10 cm, and 12 cm. respectively. Find its TSA.

Solution:

a = 10 cm

h = 12 cm

TSA = ?

L2 = H2 + (A/2)2

L2 = 144 + 25 = 169

L = 13cm

TSA = B + 1/2 PL

= a2 + 1/2 PL

=(10)2 + 1/2x 42 x 10 x 13

= 100 + 260

= 360cm2

1. The roof of a temple is in the shape of square based pyramid. The edge of the base is 7.5 m. and the slant height is 7 m. find the area of metal sheet required to cover the top of roof.

Solution:

a = 7.5 cm

L = 7m

LSA = ?

LSA = 1/2 PL = 1/2 x 4x a x L

= 1/2 x 42 x 7.5 x 7 = 14  x 7.5 = 105 m2

1. A square based pyramid is placed on a square based prism with the same base 14 cm. if the height of the prism is 9 cm. and height of the pyramid is 7 cm. find the TSA of the solid obtained by joining them.

Solution:

a = 14 cm

height of prism = 9cm

Height of pyramid = 7cm

L2 = h2 + a2

= 49 + 72

= 49 + 49

= 98

L = √98 = 7√2 cm

TSA of solid = LSA of prism + LSA of pyramid

= Ph + 1/2 PL

= 4ah + 1/2 4a x L

= 4 x 14 x9 + 1/2 x 4 x 14 x 7√2

= 504 + 28 x 7√2

= 504 + 196√2

= 14(36 + 14√2)

= 28(18 + 7√2) cm

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