Answer:
5.14 cm²
Explanation:
To find the area of the shaded region we first need to find the area of sector and then substract the area of triangle from the sector
Formulas:
- [tex] \sf \: Area \: of \: sector \: = \pi {r}^{2} \times \frac{ \theta}{360 \degree} [/tex]
- [tex] \sf \: Area \: of \: triangle \: = \frac{1}{2} ab \sin(c) [/tex]
Solution:
[tex]\sf \: Area \: of \: sector \: = \pi {r}^{2} \times \frac{ \theta}{360 \degree} [/tex]
Where,
[tex] \implies \sf \: A \: = \pi ({5}^{2}) \times \frac{ 80 \degree}{360 \degree} [/tex]
[tex] \implies \sf \: A \: = \pi ({5}^{2}) \times \frac{ 4 }{18} [/tex]
[tex] \implies \sf \: A \: = \: 25 \pi \times \frac{ 4 }{18} [/tex]
[tex] \implies \sf \: A \: = \: \frac{ 100 \pi }{18} [/tex]
[tex] \implies \sf \: A \: = \: \frac{ 100 \pi }{18} [/tex]
[tex] \implies \sf \: A \: \approx \: 17.45[/tex]
Now we can find the area of triangle.
[tex] \sf \: Area \: of \: triangle \: = \frac{1}{2} ab \sin(c) [/tex]
Where,
- a = 5cm
- b = 5cm
- c = θ = 80°
[tex] \implies \sf \: A \: = \frac{1}{2} (5)(5)\sin(80 \degree) [/tex]
[tex] \implies \sf \: A\: = \frac{25}{2} \sin(80 \degree) [/tex]
[tex] \implies \sf \: A\: \approx 12.31[/tex]
We've got the values for area of sector and area of triangle, so it's time to find the shaded area which the formula represented by;
[tex]\sf \: A_{shaded} \: = A_{sector}\: - \: A_{triangle}[/tex]
[tex]\sf \: A_{shaded} \: = 17.45\: - \: 12.31[/tex]
[tex]\sf \: A_{shaded} \: = 17.45\: - \: 12.31 [/tex]
[tex]\sf \: A_{shaded} \: = 5.14 cm {}^{2} [/tex]
Therefore, the shaded area is 5.14 square centimeters.
Learn more concerning finding shaded regions here: brainly.com/question/22307176
