Answer: [tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]
Step-by-step explanation:
PART I: Find the area of the triangle
Given information
[tex]Height=7~cm[/tex]
[tex]Base=18~cm[/tex]
Given formula
[tex]A=b\times h\times\dfrac{1}{2}[/tex]
[tex]A=Area\\b=base\\h=height\\[/tex]
Substitute values into the formula
[tex]A=(7)\times (18)\times\dfrac{1}{2}[/tex]
Simplify by multiplication
[tex]A=(7)\times 9[/tex]
[tex]A=63~cm^2[/tex]
PART II: Find the area of the rectangle
Given information
[tex]Height = 18~cm[/tex]
[tex]Base=22~cm[/tex]
Given formula
[tex]A=b\times h[/tex]
[tex]A=Area\\b=base\\h=height\\[/tex]
Substitute values into the formula
[tex]A=(22)\times (18)[/tex]
Simplify by multiplication
[tex]A=396~cm^2[/tex]
PART III: Find the area of the half-circle
Given information
Diameter = 18 cm
Given formula
[tex]A=(\dfrac{d}{2} )^2\times \pi \div2[/tex]
[tex]A=Area\\d=diameter[/tex]
Substitute values into the formula
[tex]A=(\dfrac{18}{2} )^2\times (3.14) \div2[/tex]
Simplify the fraction
[tex]A=(9 )^2\times (3.14) \div2[/tex]
Simplify the exponents
[tex]A=81\times (3.14) \div2[/tex]
Simplify by multiplication
[tex]A=254.34\div2[/tex]
Simplify by division
[tex]A=127.17~cm^2[/tex]
PART IV: Find the total area
Given formula
[tex]Total~area=Triangle+Rectangle+circle~(half)[/tex]
Substitute values into the formula
[tex]Total~area=(63)+(396)+(127.17)[/tex]
Simplify by addition
[tex]Total~area=459+(127.17)[/tex]
[tex]\Large\boxed{Total~area=586.17~cm^2}[/tex]
Hope this helps!! :)
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