Question

The curved part of this figure is a semicircle.

What is the best approximation for the area of this figure?


21+14.5π units²

10.5+14.5π units²

21+7.25π units²

10.5+7.25π units²

Answer 1

if we divide this figure into a circle and triangle
then,
area = πr²/2+1/2×3×7
area = 10.5+7.25π ans.

Answer 2

Answer:

The correct option is 4

Step-by-step explanation:

Given the figure

The curved part is semicircle whose diameter is the distance between the points (2,1) and (-5,-2) which is calculated by distance formula.

$Diameter=\sqrt((-5-2)^2+(-2-1)^2)=\sqrt58$

∴ $Radius=\frac{1}{2}\sqrt58$

Area of semicircle=$\frac{1}{2}\pi\times r^2=\frac{1}{2}\pi (\frac{58}{4})=7.25\pi units^2$

Area of Δ=$\frac{1}{2}\times base\times height= \frac{1}{2}\times 7\times 3=\frac{21}{2}=10.5units^2$

Hence, the area of figure=Area of semicircle+Area of triangle

                                         =7.25π+10.5 squnits

Hence, area of figure is 7.25π+10.5 squnits