Find the lateral and total surface area of the following pyramids.
(a) Square-based pyramid with base 6cm and slant height 14 cm.
(b) Triangular-based pyramid with base 12cm and slant height 20cm.
Solution:
Given,
(a) Square-based pyramid with base 6cm and slant height 14 cm.
Perimeter of the base = perimeter of the square base = P
P = 4 × side = 4 × 6 = 24 cm
Lateral surface area of the pyramid = 1/2 P l
where, l = slant height
LSA = 1/2 × 24 × 14 = 168 cm2
Total area of the base = Lateral surface area + Area of the base
TSA = LSA + Area
Area of the square based pyramid = side2
Area of the base = 62 = 36 cm2
∴ TSA = 168 + 36 = 204 cm2
(b) Triangular-based pyramid with base 12cm and slant height 20cm.
Perimeter of the base = perimeter of the square base = P
P = 3 × side = 3× 12 = 36 cm
Lateral surface area of the pyramid = 1/2 P l
where, l = slant height
LSA = 1/2 × 36 × 20 = 360 cm2
Total area of the base = Lateral surface area + Area of the base
TSA = LSA + Area
Area of the triangular pyramid = √3/4 s2
Area of the base = √3/4 ×(12)2 = √3/4 × 144 = 36√3 cm2
∴ TSA = 360 + 36√3 = 36(10 + √3) cm2
Find the lateral and total surface area of the following pyramids.
(a) Square-based pyramid with base 6cm and slant height 14 cm.
(b) Triangular-based pyramid with base 12cm and slant height 20cm.
Summary:
(a) The lateral and total surface area of the square-based pyramid with base 6cm and slant height 14 cm are 168 cm2 and 204 cm2 respectively.
(b) The lateral and total surface area of the triangular-based pyramid with base 12cm and slant height 20cm are 360 cm2 and 36(10 + √3) cm2 respectively.