Landon used a semicircle, a rectangle, and a right triangle, to form a figure below. Which is the best estimate of he area of the figure in square centimeters?

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calculista calculista · Answer 1 · 2019-04-21T02:42:41+02:00

Answer:

The best estimate of he area of the figure is [tex]38.28\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the figure is equal to the area of a semicircle plus the area of rectangle plus the area of a right triangle

so

[tex]A=\frac{1}{2}\pi r^{2}+LW+\frac{1}{2}bh[/tex]

we have

Semicircle

[tex]r=4/2=2\ cm[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

Rectangle

[tex]L=6\ cm[/tex]

[tex]W=4\ cm[/tex]

Triangle

[tex]b=10-6=4\ cm[/tex]

[tex]h=4\ cm[/tex]

substitute the values

[tex]A=\frac{1}{2}(3.14)(2)^{2}+(6)(4)+\frac{1}{2}(4)(4)[/tex]

[tex]A=6.28+24+8=38.28\ cm^{2}[/tex]

ewomazinoade ewomazinoade · Answer 2 · 2021-11-29T12:55:43+01:00

The area of the figure is 38.28cm².

The area of the shape is the sum of the area of the semicircle, a rectangle, and a right triangle.

Area of a semicircle = [tex]\frac{1}{2}\pi[/tex]r²

[tex]\frac{1}{2}[/tex] x 3.14 x (4/2)² = 6.28 cm²

Area of the rectangle = length x width

6 x 4 = 24 cm²

Area of the right triangle = [tex]\frac{1}{2}[/tex] x base x height

[tex]\frac{1}{2}[/tex] x (10 - 6) x 4 = 8cm²

Sum of the areas = 8 + 24 + 6.28 = 38.28cm²

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