1. 1
Slanted height
of triangle
vertex
1 A Pyramid is a solid which one of the faces is a poly_ _ _ _ _ base and the other slanted faces are
tri_ _ _ _ _ _ joined to the edges of the base.
apex apex apex apex
t _ _ _ _ _ _ _ _ _ s _ _ _ _ _ r _ _ _ _ _ _ _ _ _ _ h _ _ _ _ _ _ _ _
pyramid pyramid pyramid pyramid
If the apex is vertically above the centre of the base, the pyramid is called a r ight pyramid.
If the apex is not vertically above the centre of the base, the pyramid is called an o _ _ _ _ _ _ pyramid
A right pyramid with a regular polygonal base in known as a regular pyramid.
The corner points of a pyramid are known as vertex
apex
Vertical height
(h) of pyramid
(always at right
angle with the
base)
base
Chapter 11
Remarks:
01
UNIT: MENSURATION
TOPIC: VOLUME AND SURFACE AREA OF PYRAMID
Name: ………………………………………………….……… ( )
Class: …………..………… Date: ……………..………….
2. 2
2 Total surface area of a Pyramid = Total area of all faces
(a) The diagram below shows a square pyramid. The base has a length of 16 cm. The slight height of
each triangle is 17 cm. The pyramid has a vertical height of 15 cm.
16 cm
1 5cm
17 cm
Find the total surface area of the pyramid.
Answer (a) ……..…...……………..
(b)
The diagram below shows a rectangular pyramid. The base has a length of 12 cm and breadth of
3. 3
10 cm. The slight height of two of the triangles are 13 cm and 13.4 cm. The pyramid has a
vertical height of 12 cm.
13 cm
12 cm
13.4 cm 12 cm
10 cm
Find the total surface area of the pyramid.
Answer (b) ……..…...……………..
4. 4
2 (c)
12.1cm
10 cm
Figure 1 Figure 2
Figure 1 shows a regular octagonal pyramid and figure 2 shows the base of the pyramid.
If the slant height of the pyramid is 50 cm, find the total surface area of the pyramid.
Answer (c) ……..…...……………..
3 VOLUME OF PYRAMID
If volume of the prism =
Volume of pyramid =
height
vertical
×
area
base
×
3
1
5. 5
4 (a) The diagram below shows a square pyramid. The base has a length of 16 cm. The slight height of
each triangle is 17 cm. The pyramid has a vertical height of 15 cm.
16 cm
1 5cm
17 cm
Find the volume of the pyramid.
Answer (a) ……..…...……………..
(b) The diagram below shows a rectangular pyramid. The base has a length of 12 cm and breadth of
10 cm. The slight height of two of the triangles are 13 cm and 13.4 cm. The pyramid has a
vertical height of 12 cm.
13 cm
12 cm
13.4 cm 12 cm
10 cm
Find the volume of the pyramid.
Answer (b) ……..…...……………..
6. 6
5 The pyramid shown below has a square base of sides, 6 cm each. The slant height of the pyramid is 5
cm. Find,
6 cm
5 cm
h
(a) the vertical height h,
Answer (a) ……..…...……………..
(b) the volume,
Answer (b) ……..…...……………..
6
PQRST is a pyramid with a rectangular base where SR = 6 cm and RQ = 8 cm.
The diagonals PR and SQ intersects at U. TU is perpendicular to PQRS. Given that ST is 13 cm, find
(a) the length of SU,
Answer (a) ……..…...……………..
(b) the length of TU,
Answer (b) ……..…...……………..
(c) the volume of the pyramid.
Answer (c) ……..…...……………..
Homework Ex 11A Q2, 4, 13
