Chapter 4.3, Problem 69STP

To determine

To find: theexpression in simplest form to find the area of the triangle.

Answer to Problem 69STP

The expression that represents the area of the triangle is $6x^8$ .

Explanation of Solution

Given information:

From the figure provided in the question, it can be observed that

The base of the triangle is $4x^3$ and the height of the triangle is $3x^5$ .

Calculation : to find the area of the triangle, use the area of triangle and then substitute the base and height value and then use the product of the power property and simplify it,

  $\begin{array}{l}\text{area of triangle = }\frac{1}{2}\left(\text{base}\right)\left(\text{height}\right)\\ \text{area of triangle = }\frac{1}{2}\left(\text{4}{x}^3\right)\left(3x^5\right)\text{ [substitute]}\\ \text{area of triangle = }\frac{1}{2}\left(12x^{3+5}\right)\text{ [}{a}^m·a^n=a^{m+n}\text{and multiply}]\\ \text{area of triangle =}\left(6x^8\right)\text{ [simplify the exponents]}\end{array}$

Thus,The expression that represents the area of the triangle is $6x^8$ .