Answer to Question #148753 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.

a) 2,486.60
b) 3,464.10
c) 4,000.00
d) 8,000.00

20. Determine the total area of the prism in cm2.

a) 2,486.60
b) 3,464.10
c) 4,000.00
d) 8,000.00

(with solution pls)

Answer 1

Solution. 19. We use the prism volume formula

$$V=Ah$$

where V is volume; A is base area; h is height. The base of the prism is an equilateral triangle therefore

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

where a=10cm is edge of an equilateral triangle. Hence

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

Since the prism is right, the height of the prism is equal to the lateral edge. h=80cm. As result volume is equal to

$$V=25\sqrt{3}\times 80=2000\sqrt{3}=3464.10$$

20. Find total area using formula

$$A_{total}=2\times A_{base}+3ha$$

Since the base of the prism is an equal triangle get

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

where a=10cm is edge of an equilateral triangle. Hence

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

As result

$$A_{total}=2\times 25\sqrt{3}+3\times 80\times 10=50\sqrt{3}+2400\approx2486.60$$

Answer. 19. b) 20. a)