Chapter 12, Problem 18RP

To determine

To calculate: The volume of prism with triangular dimensions as 5, 6 and 9.

Answer to Problem 18RP

The volume of prism is $98.99$ .

Explanation of Solution

Given information:

In prism, triangular dimensions are 5, 6 and 9. Rectangular dimensions are 6 and 7.

Formula used:

We can use Heron’s Formula to determine the area of a triangle when lengths of sides are given.

The semi perimeter of triangle:

  $s=\frac{a+b+c}{2}$

a , b and c are sides of triangle

Area of triangle:

  $A=\sqrt{s(s-a)(s-b)(s-c)}$

s is semi perimeter of triangle

Volume of prism $=B\times h$

B = Base area of prism and h = height of prism

Calculation:

  

In △AED,

By heron’s formula, we get

  $s=\frac{AE+ED+AD}{2}=\frac{5+9+6}{2}=10$

Area of △AED :

  $\begin{array}{l}A=\sqrt{10(10-5)(10-9)(10-6)}\\ A=\sqrt{10\times 5\times 1\times 4}\\ A=\sqrt{200}\\ A=10\sqrt{2}\end{array}$

  $B=A(AED)=10\sqrt{2}$

h = DB = 7

Volume of prism $=B\times h$

Volume of prism $=10\sqrt{2}\times 7$

Volume of prism $=70\sqrt{2}=98.99$