Question

Find the area of an equilateral triangle whose sides are 20cm each

Answer 1

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αяєα σf αи єqυιℓαтєяαℓ тяιαиgℓє...√¾α²

ѕσ,

√¾ × 20 × 20


= 100√3¢м...

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# вє вяαιиℓу.....

Answer 2

Answer:

Let ABC be an equilateral triangle such that,

ABC = BC = CA = 20cm

Draw AD _BC

BD = DC = 10cm [perpendicular from vertex to the opposite side of an equilateral triangle bisects the opposite side].. (1)

In right triangle ADC, we have

AD² + DC² = AC² [By Pythagoras theorem]

→ AD² + (10 cm)² = (20cm)² [using (1)]

→ AD² = (20 cm)² - (10cm)² = 400 cm² - 100cm² = 300cm²

$AD = \sqrt{300cm } \: = \sqrt[10]{3} cm....(2)$

Now taking BC as the base of ∆ABC,

we have BC = base = 20cm and AD = height = 10√3 cm

$area \: of \: ∆abc \: = \frac{1}{2} (b \times \: h) = \frac{1}{2} \times BC \: \times AD \\ \\ = \frac{1}{2} \times 20cm \times 10 \sqrt{3cm} = 100 \sqrt{3 {cm}^{2} }$

Hence the area of the given equilateral triangle is

$= 100 \sqrt{3 {cm}^{2} }$

HOPE IT HELPS YOU ⛄