Question

If the Measusement of sides of triangle are 20,30, 40 find the area of triangle using Heron formula​

Answer 1

Answer:

∆PQR are the sides of triangle.

P = 20 cm

Q = 30 cm

R = 40 cm

Now,

Perimeter of ∆ = (P + Q + R)

= (20 + 30 + 40)

= 90

Semi perimeter = 90 / 2    

                           = 45 cm

By following the steps given in the picture, we get the answer as

75 × 3.8729

= 290.47 cm²

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Answer 2

As per data given in the question,

We have to determine the area of triangle by using the Heron formula.

As in question,

Three sides of triangle is given.

So, let sides of triangle are a, b and c.

a = 20 cm

b = 30 cm

c = 40 cm

So,

Perimeter of ∆ will be $= (a + b + c)= (20 + 30 + 40) = 90\:cm$

So, Semi perimeter of the triangle i.e. (s) $=\frac{90}{2}=45 \:cm$

Hence, by the Heron formula,

$Area={\sqrt{s(s-a)(s-b)(s-c)}}\\=>Area={\sqrt{45(45-20)(45-30)(45-40)}}\\=>Area={\sqrt{45 \times 25 \times 15 \times 5}}\\Area={\sqrt{(3\times 3\times 5)\times (5\times 5) \times (3\times5) \times 5}}\\Area={\sqrt{3^2\times 3\times 5^2\times 5^2\times 5}}\\Area = 3\times 5\times 5 {\sqrt{3\times5}}\\Area = 75{\sqrt{15}} \:cm^2$