A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula. -Maths 9th

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side a. Find the area of the signal board, using Heron’s formula. -Maths 9th
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Answer :

Let each side of the equilateral triangle be a. Semi-perimeter of the triangle,
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A traffic signal board indicating ‘SCHOOL AHEAD’ -Maths 9th

Description : A traffic signal board indicating ‘SCHOOL AHEAD’ -Maths 9th

Last Answer : Perimeter of the signal board, 2s = a + a + a ⇒ s = 3/2.a Area of triangle = under root (√s(s - a)(s - b)(s - c)) = under root (√3a/2(3/2.a - a)(3/2.a - a)(3/2.a - a) = under root (√3a/2 x ... = 180 cm 3a = 180 ⇒ a = 60 cm ∴ Area of signal board √3/4.a2 = √3/4 x (60)2 = 900√3 cm2

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Last Answer : (c) \(rac{a^2}{6}.\)If a' is length of the side of ΔABC, thenArea of ΔABC = \(rac{\sqrt3}{4}\,a^2\)semi-perimeter of ΔABC = \(rac{3a}{2}\)∴ Radius of in-circle = \(rac{ ext{Area}}{ ext{semi-perimeter}}\) = \( ... {( ext{diagonal})^2}{2}\) = \(rac{\big(rac{a}{\sqrt3}\big)^2}{2}\) = \(rac{a^2}{6}.\)

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Last Answer : (d) π : 3.Let each side of the equilateral Δ be a units. Then, circumradius of the circle = \(rac{ ext{side}}{\sqrt3}\) = \(rac{a}{\sqrt3}\) units∴ Area of circumcircle = \(\pi\bigg(rac{a}{\sqrt3}\bigg)^2\) = \( ... units∴ Required ratio = \(rac{rac{\pi{a}^2}{3}}{a^2}\) = \(rac{\pi}{3}\) = π : 3.

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Last Answer : Given ABCD is a quadrilateral having sides AB=6cm, BC=8cm, CD=12cm and DA=14 cm. Now. Join AC. We have, ABC is a right angled triangle at B. Now, AC2 =AB2 +BC2 [by Pythagoras theorem] Now, AC2=AB2 ... 1+6-√)cm2 =24+246=24(1+6)cm2 Hence, the area of quadrilateral is 241+6-√−−−−−−√cm2 241+6cm2 .

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