[tex]\bold{\huge{\underline{ Solution }}}[/tex]
We have,
We know that,
Area of semicircle
[tex]\bold{\pink{ = }}{\bold{\pink{\dfrac{1}{2}}}}{\bold{\pink{\pi{r^{2}}}}}[/tex]
Subsitute the required values,
[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{\dfrac{4^{2}}{2}}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{\dfrac{16}{2}}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{22}{7}}}{\sf{\times{8}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{176}{7}}}[/tex]
[tex]\bold{ = 25.142\: in.^{2}}[/tex]
Area of parallelogram
[tex]\bold{\red{ = Base }}{\bold{\red{\times{ Height }}}}[/tex]
Subsitute the required values,
[tex]\sf{ = 10 }{\sf{\times{ 6 }}}[/tex]
[tex]\bold{ = 60 \:in.^{2}}[/tex]
Thus, The area of parallelogram is 60 in.
Area of the given figure
= Area of semicircle + Area of parallelogram
Subsitute the required values,
[tex]\sf{ = 25.142 + 60 }[/tex]
[tex]\sf{ = 85.142\: in^{2}. }[/tex]
When round off to nearest Hundred
[tex]\bold{ = 85.1 in.^{2}}[/tex]
Hence, The area of the given figure is 85.1 inches² .
The area of the composite figure to the nearest hundredth is 85.12 inches squared.
The area can be defined as the space occupied by a flat shape or the surface of an object.
Therefore, the figure is a composite figure, it has a parallelogram and a semi circle.
area of the figure = area of parallelogram + area of semi circle
area of parallelogram = bh
where
b = 10 inches
h = 6 inches
area of parallelogram = 10 × 6 = 60 inches²
area of semi circle = πr² / 2
where
Therefore,
r = 8 / 2 = 4 inches
area of semi circle = 3.14 × 4² / 2
area of semi circle = 3.14 × 16 / 2
area of semi circle = 50.24 / 2
area of semi circle = 25.12 inches²
area of the figure = 60 + 25.12 = 85.12 inches²
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