Chapter 7.1, Problem 68PFA

To determine

To find: The expression that represents the area of the trapezoid.

$\begin{array}{l}\left(A\right)1.5a^{4}b\\ \left(B\right)2a^{4}b\\ \left(C\right)3a^{7}b\\ \left(D\right)5a^{3}b\end{array}$

Answer to Problem 68PFA

The required answer is option $\left(B\right)2a^{4}b$ .

Explanation of Solution

Given information:

The given diagram:

Calculation:

The area of trapezoid $=\frac{a^3+3a^3}{2}\cdot ab$

(Area of trapezoid is equal to the half of the parallel sides of the trapezoid into height between them i.e. $A=\frac{x+y}{2}\cdot h$ where “x” and “y” are the parallel side and “h” is the height)

$=\frac{4a^3}{2}\cdot ab$

(Simplify and $a^3+3a^3=4a^3$ )

$=2a^3\cdot ab$

(Simplify and $\frac{4}{2}=2$ )

$=2\left(a^3\cdot a^1\right)\left(b\right)$

(Group the coefficient and variables)

$=2\left(a^{3+1}\right)\left(b\right)$

(Product of the powers)

$=2a^{4}b$

(Simplify)