Question

topic 3: geometric applications

1. find the perimeter and area of the following:

rectangle with side labels $4x^2y$ and $13x$

1. find the area of the following:

trapezoid with side labels $9a^3b$, $2a^3b$, and height $6a^2$

Explanation:

Step1: Rectangle perimeter formula

Perimeter of rectangle = $2\times(\text{length}+\text{width})$
Substitute length $=4x^2y$, width $=13x$:
$2\times(4x^2y + 13x) = 8x^2y + 26x$

Step2: Rectangle area formula

Area of rectangle = $\text{length}\times\text{width}$
Substitute length $=4x^2y$, width $=13x$:
$4x^2y\times13x = 52x^3y$

Step3: Trapezoid area formula

Area of trapezoid = $\frac{1}{2}\times(\text{sum of parallel sides})\times\text{height}$
Substitute parallel sides $=2a^3b, 9a^3b$, height $=6a^2$:
$\frac{1}{2}\times(2a^3b + 9a^3b)\times6a^2 = \frac{1}{2}\times11a^3b\times6a^2 = 33a^5b$

Answer:

1. Perimeter: $8x^2y + 26x$; Area: $52x^3y$
2. Area: $33a^5b$