Answer:
m∠A = 31
b = 13.3
Step-by-step explanation:
Answer:
8 square units and
square units
Step-by-step explanation:
The area of the triangle ABC is 24 square units.
1. Triangles ABC and FBG are similar with scale factor
then
![\dfrac{A_{\triangle FBG}}{A_{\triangle ABC}}=\dfrac{1}{9}\Rightarrow A_{\triangle FBG}=\dfrac{1}{9}\cdot 24=\dfrac{8}{3}\ un^2.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20FBG%7D%7D%7BA_%7B%5Ctriangle%20ABC%7D%7D%3D%5Cdfrac%7B1%7D%7B9%7D%5CRightarrow%20A_%7B%5Ctriangle%20FBG%7D%3D%5Cdfrac%7B1%7D%7B9%7D%5Ccdot%2024%3D%5Cdfrac%7B8%7D%7B3%7D%5C%20un%5E2.)
2. Triangles ABC and DBE are similar with scale factor
then
![\dfrac{A_{\triangle DBE}}{A_{\triangle ABC}}=\dfrac{4}{9}\Rightarrow A_{\triangle DBE}=\dfrac{4}{9}\cdot 24=\dfrac{32}{3}\ un^2.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20DBE%7D%7D%7BA_%7B%5Ctriangle%20ABC%7D%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5CRightarrow%20A_%7B%5Ctriangle%20DBE%7D%3D%5Cdfrac%7B4%7D%7B9%7D%5Ccdot%2024%3D%5Cdfrac%7B32%7D%7B3%7D%5C%20un%5E2.)
3. Thus, the area of the quadrilateral DFGE is
![A_{DFGE}=A_{\triangle DBE}-A_{\triangle FBG}=\dfrac{32}{3}-\dfrac{8}{3}=8\ un^2.](https://tex.z-dn.net/?f=A_%7BDFGE%7D%3DA_%7B%5Ctriangle%20DBE%7D-A_%7B%5Ctriangle%20FBG%7D%3D%5Cdfrac%7B32%7D%7B3%7D-%5Cdfrac%7B8%7D%7B3%7D%3D8%5C%20un%5E2.)
and the area of the quadrilateral ADEC is
![A_{ADEC}=A_{\triangle ABC}-A_{\triangle DBE}=24-\dfrac{32}{3}=\dfrac{40}{3}\ un^2.](https://tex.z-dn.net/?f=A_%7BADEC%7D%3DA_%7B%5Ctriangle%20ABC%7D-A_%7B%5Ctriangle%20DBE%7D%3D24-%5Cdfrac%7B32%7D%7B3%7D%3D%5Cdfrac%7B40%7D%7B3%7D%5C%20un%5E2.)
R = 13.1
so
<span>diameter = 13.1 x 2 = 26.2 km
</span>circumference = 2 pi r = 26.2 pi km
or
circumference = 26.2 x 3.14 = 82.27 km