Question

The base of the right prism is an equilateral triangle. The area of the base is 1,560 cm2. If the altitude of the prism is 5 meters,

____________________What is the base edge of the prism in cm?


____________________What is the lateral area of the prism in m2?


_____________________What is the volume of the prism in m3?

Answer 1

Base area (B) = 1560 cm² = 0.156 m²

Base area (B) $= \frac{\sqrt{3}}{4}a^2$

a - the base edge

$0.156 = \frac{\sqrt{3}}{4}a^2 \\ a^2 = \frac{0.624}{\sqrt{3}} \\ a = \sqrt{0.360} \\ a = 0.6 \; m = 60 \;cm$

The base edge of the prism is 60 cm.

Lateral area of the prism $= h \times P$

P - perimeter of triangle

In this case P

$P = 3a \\ P = 3 \times 0.6 = 1.8 \;m \\ h = 5 \;m$

Lateral area of the prism $= 5 \times 1.8 = 9 \; m^2$

Volume of prism

$V = B \times h \\ V = 0.156 \times 5 = 0.78 \;m^3$

The volume of the prism is 0.78 m³