Q:

Find the perimeter and the area of the composite figurea. What is the approximate perimeter of the concrete region? Use 3.14 for πb. What is the exact area of the concrete region? Leave answers in terms of π.

Accepted Solution

A:
Answer:Part A) The approximate perimeter of the concrete region is [tex]P=64.66\ yd[/tex]Par B) The exact area of the concrete region is [tex]A=(8\pi+162.4)\ yd^{2}[/tex]Step-by-step explanation:Part A) What is the approximate perimeter of the concrete region?we know thatThe perimeter of the composite figure is equal to[tex]P=\pi r+2(15.2)+ 11.5+10.2[/tex]The radius of semicircle is[tex]r=8/2=4\ yd[/tex]substitute[tex]P=(3.14)(4)+2(15.2)+ 11.5+10.2=64.66\ yd[/tex]Part B) What is the exact area of the concrete region?we know thatThe area of the composite figure is equal to the area of semicircle plus the area of rectangle plus the area of triangleso[tex]A=\frac{1}{2} \pi r^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex]The radius of semicircle is[tex]r=8/2=4\ yd[/tex][tex]A=\frac{1}{2} \pi (4)^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex][tex]A=8\pi+121.6+40.8[/tex][tex]A=(8\pi+162.4)\ yd^{2}[/tex]