5 A circle is inscribed in the square ABCD as shown in the figure The length - Maths - Areas Related to Circles

Question

5 A circle is inscribed in the square ABCD as shown in the figure
The length of the side of the square is 6 cm long What will be the
area of the equilateral triangle EFG?
1     10 598   c m 2 2     11 097   c
m 2 3     11 988   c m 2 4     12 187
  c m 2

Brijendra Pal · Accepted Answer

Hi,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5ab530ddbdb90%20png"
style="width: 214px; height: 182px;">
Here side of square will be diameter of circle 2r = 6 cm r  = 3 cm Now if EGF is an equilateral triangle then FM is here perpendicular to EG and we know that altitude is the median and also centroid, incenter , orthocenter all lies at O in equilateral triangle so angle FEG = 60 degreeso O is the centroid so it will divide median in 2:1 and we have already calculated radius r = FO = 3 cm so FO = 23FM   using ratio FO:OM= 2:1FM = 32FO = 32×3 = 92 cm now in right triangle FME, tan60 = FMEMEM = FMtan60=923 cm now since M is mid point of EG so EG = 2 EM = 93  cm so area of triangle EFG = 12 base ×height= 12×93×92=8143=814×1
732= 11 691 cm2

5. A circle is inscribed in the square ABCD as shown in the figure. The length of the side of the square is 6 cm long. What will be the area of the equilateral triangle EFG? 1 . 10 . 598 c m 2 2 . 11 . 097 c m 2 3 . 11 . 988 c m 2 4 . 12 . 187 c m 2

5. A circle is inscribed in the square ABCD as shown in the figure. The length of the side of the square is 6 cm long. What will be the area of the equilateral triangle EFG?
$1 . 10.598 c m^{2} 2 . 11.097 c m^{2} 3 . 11.988 c m^{2} 4 . 12.187 c m^{2}$