Question

I need help with number 16 can I please get help?

Answer 1

We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.

We break apart the figure as shown below:

First,

Area of Triangle = 0.5 * base * height

Area of Rectangle = base * height

Now, let's find each of the Areas A through D:

Area of A:

To find the base of this triangle, we have to use pythagorean theorem. By which we can write:

`b^2+4^2=6^2`

Where b is the base. let's solve for b:

`\begin{gathered} b^2+16=36 \\ b^2=36-16 \\ b^2=20 \\ b=\sqrt[]{20} \\ b=\sqrt[]{4}\sqrt[]{5} \\ b=2\sqrt[]{5} \end{gathered}`

Area is

`\begin{gathered} 0.5\cdot\text{base}\cdot\text{height} \\ =(1)/(2)\cdot2\sqrt[]{5}\cdot4 \\ =4\sqrt[]{5} \end{gathered}`

Area of B:

This is a rectangle with base = 10 and height 4, so the area is:

Area = 4 * 10 = 40

Area of C:

Area of C is exactly same as area of B, base is 10 and height is 4. So,

Area = 4 * 10 = 40

Area of D:

Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:

`\begin{gathered} b^2+4^2=4.5^2 \\ \end{gathered}`

Solving for b:

`\begin{gathered} b^2+4^2=4.5^2 \\ b^2+16=20.25 \\ b^2=(17)/(4) \\ b=\frac{\sqrt[]{17}}{\sqrt[]{4}} \\ b=\frac{\sqrt[]{17}}{2} \end{gathered}`

Now, area of triangle is:

`A=(1)/(2)(\frac{\sqrt[]{17}}{2})(4)=\sqrt[]{17}`

Area of whole figure:

`\begin{gathered} 4\sqrt[]{5}+40+40+\sqrt[]{17} \\ =80+4\sqrt[]{5}+\sqrt[]{17} \end{gathered}`

Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:

`3*(80+4\sqrt[]{5}+\sqrt[]{17})\approx279.202`

It will cost around:

$279.20