Question

This figure is made up of a triangle and a semicircle.
What is the area of the figure?
Use 3.14 for π.

Enter your answer, as a decimal, in the box.

___units²

Answer 1

The answer is:  "41 .12"  units²  . 
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Explanation:
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The combined area = the area of a semi-circle (half-circle); PLUS the area of the triangle.
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The area, "A", of a triangle:

A = (b * h) / 2 ;  in which b = base; and "h = perpendicular height" ; 

From the diagram:  "b = 8" ;  "h = distance from "(4, 1)" to "(4, 5)" = 4 ;

A = (b * h) / 2  = (8 * 4) / 2 = 32/2 = 16 units²
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The area of the "half of a circle" :

Note: The area, "A" ; of a [FULL] circle:

A = $\pi$  * r²  ; 

          in which:  r = radius = 4 ; {as shown in figure attached;

  We are told to use the approximation of "3.14" for $\pi$ ; 

A = (3.14) * 4²  = 3.14 * 16 ;

To get the area of "one-half" that circle; we divide this value by "2" ; 

Area of "half-circle" = $\frac{3.14 * 16}{2}$  ;

The "$\frac{16}{2}$" result in "8" ; 

And we know have:   "3.14 * 8" ; 

3.14 * 8 = 25.12 units²
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The total area of the figure =  

16 units² + 25.12 units² =
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          41 .12 units²  .
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Answer 2

41.12 units^2

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