Question

What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.

Answer 1

The company's sign has two(2) congruent trapezoids and two(2) congruent right angled triangle.

The area of the figure is:

`A_{\text{figure}}=2A_{\text{trapezoid}}+2A_{\text{triangle}}`

The area of a trapezoid is given by the formula:

`\begin{gathered} A_{\text{trapezoid}}=(1)/(2)(a+b)h \\ \text{where a and b are opposite sides of the trapezoid} \\ h\text{ is the height} \end{gathered}`

Thus, we have:

`\begin{gathered} A_{\text{trapezoid}}=(1)/(2)(1(1)/(2)+3)2 \\ A_{\text{trapezoid}}=(1)/(2)(1.5+3)2 \\ A_{\text{trapezoid}}=(1)/(2)*4.5*2=4.5m^2 \end{gathered}`

Area of a triangle is given by the formula:

`A_{\text{triangle}}=(1)/(2)* base* height`

Thus, we have:

`\begin{gathered} A_{\text{triangle}}=(1)/(2)*2*1(1)/(2) \\ A_{\text{triangle}}=(1)/(2)*2*1.5=1.5m^2 \end{gathered}`

Hence, the area of the company's sign is:

`\begin{gathered} A=(2*4.5)+(2*1.5) \\ A=9+3=12m^2 \end{gathered}`