Answer to Question #148944 in Geometry for solid mensuration

Question

The base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80cm.

19. Find its volume in cm3.
20. Determine the total area of the prism in cm2

Answer 1

Solution. The area of a equilateral triangle, which is the base of the prism

$$A=\frac{a^2\sqrt{3}}{4}$$

where a=10 cm is edges of the equilateral triangle.

Therefore

$$A=\frac{10^2\sqrt{3}}{4}=25\sqrt{3}cm^2$$

Find the volume of a right prism as

$$V=Ah$$

where A is area of the base of the prism; h=80cm is lateral edge of the prism.

Hence

$$V=80\times25\sqrt{3}=2000\sqrt{3}cm^3\approx3464.1cm^3$$

Find the total area of the prism using formula

$$A_{total}=3ah+2A_{base}$$

$$A_{total}=3\times 10\times80+2\times 25\sqrt{3}=2400+50\sqrt{3}\approx2486.6cm^2$$

Answer.

$$V=2000\sqrt{3}cm^3\approx3464.1cm^3$$

$$A_{total}=2400+50\sqrt{3}\approx2486.6cm^2$$