Everything Maths Grade 10

Worked example 8: Finding the surface area of a triangular pyramid

QUESTION

Find the surface area of the following triangular pyramid (correct to one decimal place):

|

10 cm

6 cm

SOLUTION

Step 1: Find the area of the base

area of base triangle=^12 bhb

To find the height of the base triangle(hb)we use the theorem of Pythagoras:

3 cm

hb

6 cm

62 = 3^2 +h^2 b

)hb=

√

62 32

= 3

p

3

)area of base triangle=

1

2

 6  3

p

3

= 9

p

3 cm^2

Step 2: Find the area of the sides

area of sides= 3

(

1

2

bhs

)

= 3

(

1

2

 6  10

)

=90 cm^2

434 13.3. Right pyramids, right cones and spheres