Question

the length of a rectangle is 16.2 inches, and the area of the rectangle is 202.5 square inches. what is the width of the rectangle in inches?

1. the dimensions of a patio shaped like a trapezoid are given in meters. find the area of the trapezoid in square meters?
2. a right rectangular prism with a square base is shown. the volume of the prism is 325 square units. what is the height, h, of the prism?

Explanation:

Step1: Recall rectangle area formula

The area formula of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. We need to find $w$, so we can rewrite the formula as $w=\frac{A}{l}$.

Step2: Substitute given values

Given $A = 202.5$ square - inches and $l = 16.2$ inches. Then $w=\frac{202.5}{16.2}=12.5$ inches.

Step3: Recall trapezoid area formula

The area formula of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. Here $a = 13$ m, $b = 7$ m and $h = 9$ m.

Step4: Calculate trapezoid area

$A=\frac{(13 + 7)\times9}{2}=\frac{20\times9}{2}=90$ square meters.

Step5: Recall rectangular - prism volume formula

The volume formula of a right - rectangular prism with a square base is $V=B\times h$, where $V$ is volume, $B$ is the area of the base and $h$ is the height. The base is a square with side length $s = 5$ units, so the area of the base $B=s^{2}=5^{2}=25$ square units.

Step6: Solve for height

We know $V = 325$ square units and $B = 25$ square units. From $V=B\times h$, we can solve for $h$ as $h=\frac{V}{B}=\frac{325}{25}=13$ units.

Answer:

1. Width of rectangle: 12.5 inches
2. Area of trapezoid: 90 square meters
3. Height of rectangular prism: 13 units