Chapter 12.8, Problem 18PPS

a.

To determine

To determine the perimeter of the base of Pyramid A.

Answer to Problem 18PPS

  $24$ centimeter

Explanation of Solution

Given:

  

Pyramids shown are congruent

Formula used:

Perimeter of a shape $=$ Sum of all the sides

Calculation:

  

If the shapes are congruent then the scale factor ratio is same. Since the pyramids are congruent, then there scale factor is 1:1.

The base of the pyramids is in the shape of a right triangle as the angles are already marked in the figure.

The base of the base of pyramid B is 8 which is same for pyramid A.

Finding the side of the pyramid A.

Let’s consider the side as $h$ .

  $\Rightarrow h^2+8^2={10}^2$

  $\Rightarrow h^2=100-64$

  $\Rightarrow h=\sqrt{36}$

  $\Rightarrow h=6\text{ centimeter}$

The perimeter of the base of Pyramid A is 10 + 8 + 6 or 24 centimeter.

Conclusion:

Therefore, the perimeter of the base of Pyramid A is $24$ centimeter.

b.

To determine

To determine the area of the base of Pyramid B.

Answer to Problem 18PPS

  $24{\text{ centimeter}}^2$

Explanation of Solution

Given:

  

Pyramids shown are congruent

Formula used:

Area of triangle $=\frac{1}{2}\times b\times h$$\left[b=\text{base and }h=\text{height}\right]$

Calculation:

  

Pyramids shown are congruent.

From the previous subpart part the bases of the pyramids are right triangles with base 8 cm and height 6 cm.

Area of triangle $=\frac{1}{2}\times b\times h$$\left[b=\text{base and }h=\text{height}\right]$

  $=\frac{1}{2}\times 6\times 8$

  $=\frac{1}{2}\times 48$

  $=24{\text{ centimeter}}^2$

Conclusion:

Therefore, the area of the base of Pyramid B is $24{\text{ centimeter}}^2$ .

c.

To determine

To determine the volume of Pyramid B.

Answer to Problem 18PPS

  $104{\text{ centimeter}}^3$

Explanation of Solution

Given:

  

Pyramids shown are congruent

Formula used:

Volume of pyramid $=\frac{1}{3}\times B\times h$$\left[B=\text{area and }h=\text{height}\right]$

Calculation:

  

Pyramids shown are congruent.

From the previous subparts part the bases of the pyramids are right triangles area is $24{\text{ centimeter}}^2$ and height of pyramid is same as pyramid A that is 13 centimeter.

Volume of pyramid $=\frac{1}{3}\times B\times h$$\left[B=\text{area and }h=\text{height}\right]$

  $=\frac{1}{3}\times 24\times 13$

  $=104{\text{ centimeter}}^3$

Conclusion:

Therefore, the volume of Pyramid B is $104{\text{ centimeter}}^3$ .