Answer to Question #148228 in Trigonometry for yui

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