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Advocard [28]
3 years ago
9

The area of a circle is 80 square inches. Find the area of the sector whose central angle is 45 degrees

Mathematics
2 answers:
Pie3 years ago
7 0
The whole circle (in terms of area) is 360 degrees. 
Area of Sector = (angle / 360) * Area of the entire circle
Area of Sector = (45 / 360) * 80 in^2
Area of sector = (1/8) * 80 in^2
Area of sector = 10 in^2
Kisachek [45]3 years ago
4 0
We know that whole circle has 360⁰.
We can write a proportion
80 in² --------360 ⁰
x in² --------45⁰

x=(80*45)/360 =(8*45)/36 = 10 in²
<span>The sector whose central angle is 45 degrees has are 10 in².</span>

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Answer:

Quadrilateral FSHB∼quadrilateral KTWJ.

Step-by-step explanation:

Given two quadrilaterals we have to prove these two similar.

The two quadrilaterals are similar if the corresponding sides of these are proportional then only the quadrilateral are proportional i.e

∴ \frac{FS}{KT}=\frac{SH}{TW}=\frac{HB}{WJ}=\frac{BF}{JK}

If the above condition satisfied then the quadrilateral are similar.

Let us find these ratios

\frac{FS}{KT}=\frac{28}{21}=1.333

\frac{SH}{TW}=\frac{24}{18}=1.333

\frac{HB}{WJ}=\frac{18}{13.5}1.333

\frac{BF}{JK}=\frac{18}{13.5}1.333

All ratios are equal.

Hence, the corresponding sides and angles of these two quadrilaterals are proportional implies that these two are similar i.e quadrilateral FSHB∼quadrilateral KTWJ.




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