Question

EXERCISE 1
LEVEL-1
1. Find the area of a triangle whose sides are respectively 150 cm 120 cm and 200 cm
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Answer 1

• Area of triangle is 8966.57 cm².

Step-by-step explanation:

Given:-

• Sides of triangle are 150 cm, 120 cm and 200 cm.

To find:-

• Area of triangle.

Solution:-

Here,

We will use Heron's formula for finding area of triangle because height of triangle is not given.

Heron's formula is :

Area of triangle = √s(s - a)(s - b)(s - c)

In which,

• s is semi-perimeter.
• a, b and c are sides of triangle.

Formula for semi-perimeter is

Semi-perimeter = Perimeter/2

According to question,

s = 150 + 120 + 200/2

s = 470/2

s = 235

Area of triangle:

= √235(235 - 150)(235 - 120)(235 - 200)

= √235 × 85 × 115 × 35

= √5 × 47 × 5 × 17 × 5 × 23 × 5 × 7

= 5 × 5 × √47 × 17 × 23 × 7

= 25 × √128639

= 25 × 358.66

= 8966.57

Therefore,

Area of triangle is 8966.57 cm².

Answer 2

♣GIVEN♣

• Sides of a triangle = 150 cm, 120 cm and 200 cm

♣TO FIND♣

• The area of the triangle = ?

♣SOLUTION♣

• Hence here we use the Heron's Formula to find the area of the triangle. It was given by the Greek mathematician Hero :-

Let a, b and c be the sides of the triangle.

By first condition :-

$\large \boxed{ \boxed{ \sf{ \mapsto{ s= \bf{ \dfrac{1}{2} \bigg(a + b + c \bigg)}}}}}$

NOTE :- S is a constant here

→ s = 1/2(150 + 120 + 200)

→ s = 1/2(470)

→ s = 470/2

→ s = 235

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By second condition :-

$\large{ \boxed{ \boxed{ \sf{ \mapsto{Area = \bf{\sqrt{s \bigg(s - a \bigg) \bigg(s - b \bigg) \bigg(s - c \bigg)}} }}}}}$

→ Area = √{235(235 - 150)(235 - 120)(235 - 200)}

→ Area = √(235 × 85 × 115 × 35)

→ Area = √80,399,375

→ Area = 8,966.57 (approx value)

____________________________

♣ANSWER♣

• The area of the triangle is 8966.57 (approximately)