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The area of rectangular surfaces of a triangular prism having base sides 9 cm. 10 and 17 cm is 864 cm³. Calculate the height of the prism.​

User Zae
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8.7k points

2 Answers

1 vote

Answer: To calculate the height of the triangular prism, we'll first need to find the area of the rectangular surfaces. The formula for the volume (V) of a triangular prism is given by:

V = (1/2) * base * height * length,

where:

base = base of the triangular base (in this case, it's the side with length 9 cm),

height = height of the triangular base (we need to find this),

length = length of the prism (in this case, it's the side with length 17 cm).

We are given that the volume of the prism is 864 cm³, so we can write the equation as:

864 = (1/2) * 9 * height * 17.

Now, let's solve for the height:

864 = (1/2) * 9 * height * 17

864 = 76.5 * height

Divide both sides by 76.5:

height = 864 / 76.5

height = 11.294 cm (approximately).

The height of the triangular prism is approximately 11.294 cm.

User XiaoFangyu
by
8.1k points
5 votes

Answer:

the required height is 24 cm

The area of rectangular surfaces of a triangular prism having base sides 9 cm. 10 and-example-1
User Aristedes
by
7.5k points
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