An architect is planning to make two triangular prisms out of iron. The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.
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(a) What is the scale factor from ∆ABC to ∆DEF?

(b) Suppose the height of the prism made by ∆ABC is 15 centimeters. What is the volume of the prism made by ∆ABC? Remember to show your work.

(c) Suppose the volume of the prism made by ∆ABC is 4459 cm^3. What is the volume of the prism made by ∆DEF? Remember to show your work.

a) 5/7

b) 4459 cm cube

c) 2275 cm cube

Step-by-step explanation:

Step 1 :

a)

The Side AB (28 cm) has been scaled to side DE (20 cm)

Let x b the scale factor.

Then we have 28 *x = 20

=> x = 20/28 = 5/7

Hence the scale factor is 5/7

Step 2 :

b)

Given the height of the triangular prism is 15 cm

Volume = ( 1/2 ) * base* height of the triangle * height of the prism

= (1/2)* 21*28*15 = 4410 cm cube.

Step 3 :

c)

Given volume of the triangular prism with base ABC is 4459 cm cube

The scale factor is 5/7

Hence the volume of the prism with DEF as base is

4459 * (5/7)*(5/7) = 2275 cm cube.

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