Question

1.
Find the area of of a triangle; whose sides
are :

(iii) 21 m, 28 m and 35 m​

Answer 1

Answer:

The area of triangle is 294m²

SidesofΔare

a=21m

b=28m

c=35m

s=

2

a+b+c

=

2

21+28+35

(Simplifying we get)

s=

2

84

=30

AreaofΔ=

S(S−a)(S−b)(S−c)

(formula)

=

42(42−21)(42−28)(42−35)

=

42×21×14×7

=

7×3×3×3×7×2×7×7

7×7×7×7×3×3×2×2

Ans=7×7×3×2=294m

2

Answer 2

★ Given :

• Side of the triangle, a = 21 m
• Side of the triangle, b = 28 m
• Side of the triangle, c = 35 m

★ To find :

• Area of the triangle with the sides 21 m, 28 m and 35 m.

★ Formula required :

Area of a Scalene triangle :

⠀⠀⠀⠀⠀⠀⠀⠀⠀A = √[s(s - a)(s - b)(s - c)]

Where :

A = Area of the triangle

a, b and c = Sides of the triangle

s = Semi-perimeter of the triangle

Here,

Semi perimeter = s = (a + b + c)/2

★ Solution :

Area of the triangle :

Let's find out the semi-perimeter of the triangle :

Semi perimeter :

⇒ s = (a + b + c)

⇒ s = (21 + 28 + 35)/2

⇒ s = 84/2

⇒ s = 42

∴ s = 42 m

The semi-perimeter of the triangle is 42 m.

Now using the formula for area of a triangle and substituting the values in it, we get :

==> A = √[s(s - a)(s - b)(s - c)]

==> A = √[42 × (42 - 21) × (42 - 28) × (42 - 35)]

==> A = √(42 × 21 × 14 × 7)

==> A = √86436

==> A = 294

∴ A = 294 m²

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