Question

directions: use the area formulas to find each missing measure. 13. a parallelogram with an area of 211.41 m² has a base that measures 24.3 m. find its height. 15. find the length of the second bas a 17. a semicircle has an area of 76.97 km². find its radius. 19. 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.

Step2: Solve for height

We know that $A = 211.41\ m^{2}$ and $b = 24.3\ m$. Rearranging the formula for $h$, we get $h=\frac{A}{b}$. Substituting the given values, $h=\frac{211.41}{24.3}=8.7\ m$.

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.

Step2: Solve for radius

We know that $A = 76.97\ km^{2}$. First, we can rewrite the formula for $r$ as $r^{2}=\frac{2A}{\pi}$. Then $r=\sqrt{\frac{2A}{\pi}}$. Substituting $A = 76.97\ km^{2}$ and $\pi\approx3.14$, we have $r^{2}=\frac{2\times76.97}{3.14}=\frac{153.94}{3.14} = 49$. So $r = 7\ km$.

Step1: Recall area formula for triangle

The area formula of a triangle is $A=\frac{1}{2}bh$. For an equilateral triangle with side length $s = 15\ ft$, the base $b = 15\ ft$ and the height $h=\frac{\sqrt{3}}{2}s=\frac{\sqrt{3}}{2}\times15\ ft$. But if we assume it's just a general triangle and we don't know the height, and we assume it's an isosceles or equilateral triangle for simplicity and use the formula $A=\frac{\sqrt{3}}{4}s^{2}$ (for equilateral triangle), substituting $s = 15\ ft$, we get $A=\frac{\sqrt{3}}{4}\times15^{2}=\frac{\sqrt{3}}{4}\times225\approx\frac{1.732}{4}\times225 = 97.425\ ft^{2}$.

Step2: Calculate cost

The cost of the glass is $\$18.75$ per square - foot. So the total cost $C=A\times18.75$. Substituting $A = 97.425\ ft^{2}$, we get $C=97.425\times18.75=\$1826.67$.

Answer:

$8.7\ m$

17.