Question

Find the volume and surface area of a pyramid with a triangular base with each edge 6 cm and a height of 10 cm. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Volume $=\frac{1}{3}\times areaofbase\times h$

To work out area of base triangle

$A{B}^2=6^2-3^2$ (Using Pythagoras Theorem)

$AB=\sqrt{27}$

$\therefore$ Volume $=\frac{1}{3}\times (\frac{1}{2}\times 6\times \sqrt{27})\times 10$

$=30\sqrt{3}$

$=51.96c{m}^3$

Surface area = Area of the base + Area of 3 other Triangles

$=9\sqrt{3}+3(\frac{1}{2}\times 6\times \sqrt{103})$

$=106.93c{m}^2$

(Since slant height $=\sqrt{103})$