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

41.12 units^2

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Answer 2

The answer is: "41 .12" units² .
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Step-by-step 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" =
`(3.14 * 16)/(2)` ;

The "
`(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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