Question

12.
directions: use the area formulas to find each missing measure.

1. a parallelogram with an area of 211.41 m² has a base that measures 24.3 m. find its height.
2. find the length of the second bar
3. a semicircle has an area of 76.97 km². find its radius.
4. scott needs to replace a broken window at his house. the window is shaped like a triangle with dimensions shown below. if glass costs $18.75 per square foot, how much will the replacement window cost?

15 ft

Explanation:

13.

Step1: Recall area formula for parallelogram

The area formula of a parallelogram is $A = b\times h$, where $A$ is the area, $b$ is the base and $h$ is the height. We need to solve for $h$.

Step2: Rearrange the formula to solve for $h$

$h=\frac{A}{b}$. Given $A = 211.41$ m² and $b = 24.3$ m.

Step3: Calculate the height

$h=\frac{211.41}{24.3}=8.7$ m

Step1: Recall area formula for semi - circle

The area formula of a semi - circle is $A=\frac{1}{2}\pi r^{2}$, where $A$ is the area and $r$ is the radius. We need to solve for $r$.

Step2: Rearrange the formula to solve for $r$

First, multiply both sides of the equation $A=\frac{1}{2}\pi r^{2}$ by $2$ to get $2A=\pi r^{2}$. Then $r^{2}=\frac{2A}{\pi}$. Taking the square - root of both sides, $r=\sqrt{\frac{2A}{\pi}}$. Given $A = 76.97$ km².

Step3: Calculate the radius

$r=\sqrt{\frac{2\times76.97}{\pi}}=\sqrt{\frac{153.94}{\pi}}\approx\sqrt{\frac{153.94}{3.14}}=\sqrt{49}=7$ km

Step1: Recall area formula for triangle

The area formula of a triangle is $A=\frac{1}{2}bh$. Assume the base $b = 15$ ft. If the height of the triangle is not given, assume it is an equilateral triangle, and for an equilateral triangle with side length $s = 15$ ft, the height $h=\frac{\sqrt{3}}{2}s=\frac{\sqrt{3}}{2}\times15\approx12.99$ ft. Then $A=\frac{1}{2}\times15\times12.99 = 97.425$ ft².

Step2: Calculate the cost

The cost of the glass is $\$18.75$ per square - foot. So the total cost $C=18.75\times A$. Substitute $A = 97.425$ into the formula: $C=18.75\times97.425=\$1826.72$

Answer:

$8.7$ m

17.