Question

The sides of the base of a pentagonal prism measure 3, 5, 6, 8, and 9 cm, respectively. A second prism similar to the first has its shortest side equal to 2 cm, and lateral area of 144 cm2 . What is the altitude of the first prism?

Answer 1

Make me the Branalist

Make me the Branalist

Answer 2

Concept:

The pentagonal prism is a prism with a pentagonal base.

Given:

The sides of the base of a pentagonal prism measure 3, 5, 6, 8, and 9 cm.

Shortest side of second prism is 2 cm.

Later area of second prism i 144 cm²

Find:

the altitude of the first prism

Solution:

First prism:

Perimeter of the pentagonal base:

3 + 5 + 6 + 8 + 9 = 31 cm

Now, the second prism is similar to the first one.

So, the similarity coefficient is: 2/3 (the second to the first)

Second Prism:

Perimeter of the pentagonal base: (2/3)×31=62/3 cm.

Lateral area= 144 cm²

Height=144÷(62/3)=216/31 cm.

Then, the altitude of the first prism = (3/2)×(216/31)=10.4516 cm (approx.)

Therefore, the altitude of the first prism is 10.4516 cm.

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