Question

10. The area of an equilateral triangle ABC is 17320.5
cm? With each vertex of the triangle as centre, a
circle is drawn with radius equal to half the length
of the side of the triangle (see Fig. 12.28). Find the
area of the shaded region. (Use it = 3.14 and
13 = 1.73205)​

Answer 1

Answer:

where is shaded region??

Answer 2

Step-by-step explanation:

GIVEN:-

AB= BC = AC

AREA OF EQUILATERAL △ ABC = 17320.5cm^2

TO FIND:-

THE AREA OF THE SHADED REGION

STEPS:-

AREA OF EQUILATERAL △ ABC = 17320.5cm^2

$∴ \frac{ \sqrt{3} }{4} = ab ^{2} = 17320.5cm ^{2} \\ ∴ab \: = 200cm$

AB = 2AD

∴AD = 100CM ( RADIUS)

AREA OF SECTOR DAE + AREA OF SECTOR DBF + AREA OF SECTOR FCE

$area \: of \: sector = \frac{θ}{360} \times \pi \times r {}^{2} \\ = 3 \times \frac{60}{360 } \times 3.14 \times 100 \times 1000 \\ = 15700cm {}^{2}$

∴ AREA OF THE SHADED REGION = AREA OF EQUILATERAL TRIANGLE − AREA OF ALL SECTORS

$=17320.5 − 15700 \\ = 1620.5cm {}^{2}$