Question

1)Find the area of a triangle whose sides are 8 cm, 5 cm and 4 cm using herons formula

2)Find the area of a triangle whose sides are 40 cm,14 cm and 28 cm.using herons formula

correct and best ans brainliest

formula:
$\sqrt{s(s - a) (s - b )(s - c)}$
s =semiperimeter​

Answer 1

Question 1 :

Given:

Let a , b ,c be the sides of the given triangle and s is the semi-perimeter:

• a = 8 cm

• b = 5 cm

• c = 4 cm

To find out:

Find the area of a triangle?

Solution:

We know that,

s = 1/2 ( a + b + c )

= 1/2 ( 8 + 5 + 4 )

= 1/2 × 17

= 17/2

Now,

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

= √ 17/2 ( 17/2 - 8 ) ( 17/2 - 5 ) ( 17/2 - 4 )

= √ 17/2 × 1/2 × 7/2 × 9/2

= √ 1071/16

= 8.18 cm² ( approx)

Question 2:

Given:

Let a , b ,c be the sides of the given triangle and s is the semi-perimeter:

a = 40 cm

b = 14 cm

c = 28 cm

To find out:

Find the area of a triangle?

Solution:

We know that,

s = 1/2 ( a + b + c )

= 1/2 ( 40 + 14 + 28 )

= 1/2 × 82

= 41 cm

Now,

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

= √ 41 ( 41 - 40 ) ( 41 - 14 ) ( 41 - 28 )

= √ 41 × 1 × 27 × 13

= √ 14391

= 119.96 cm² ( approx)

Answer 2

QUESTION:

❶ Find the area of a triangle whose sides are 8 cm, 5 cm and 4 cm using herons formula

GIVEN:

• $\bf{ \: a = 8 \: cm \: \star }$
• $\bf{ \: b = 5 \: cm \: \star }$
• $\bf{ \: c = 4 \: cm \: \star }$

TO FIND:

• What is the area of the triangle ?

SOLUTION:

We have to find the area of triangle using Heron's formula

Firstly, we need to find the semi - perimeter of the triangle

$\large\bf{\star \: s = \frac{a+b+c}{2} \: \star }$

Put the value of a,b, and c in the formula:

$\sf{ s = \frac{8+5+4}{2} = \cancel\frac{17}{2}}$

$\large\bf{ \star \: s = 8.5\: cm \:\star }$

To find the area of triangle, we use the formula:-

$\large\bf{ \star \: \sqrt{s(s-a)(s-b)(s-c)} \: \star }$

According to question:-

$\sf{\implies Area = \sqrt{ 8.5 (8.5 - 8 ) (8.5-5)(8.5-4)}}$

$\sf{\implies Area = \sqrt{ 8.5 \times 0.5 \times 3.5 \times 4.5}}$

$\sf{\implies Area = \sqrt{ 66.9375}}$

$\bf{\implies \star \: Area = 8.18 \: cm^2 \:(approx)\: \star }$

❝ Hence, the area of triangle is 8.18 cm² approx. ❞

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QUESTION:

❷ Find the area of a triangle whose sides are 40 cm,14 cm and 28 cm. using Heron's formula

GIVEN:

• $\bf{ \: a = 40 \: cm \: \star }$
• $\bf{ \: b = 14 \: cm \: \star }$
• $\bf{ \: c = 28 \: cm \: \star }$

TO FIND:

• What is the area of the triangle ?

SOLUTION:

We have to find the area of triangle using Heron's formula

Firstly, we need to find the semi - perimeter of the triangle

$\large\bf{\star \: s = \frac{a+b+c}{2} \: \star }$

Putting the value of a,b, and c in the formula, we get

$\sf{ s = \frac{40+14+28}{2} = \cancel\frac{82}{2}}$

$\large\bf{ \star \: s = 41\: cm\: \star }$

To find the area of triangle, we use the formula:-

$\large\bf{ \star \: \sqrt{s(s-a)(s-b)(s-c)} \: \star }$

According to question:-

$\sf{\implies Area = \sqrt{ 41 (41-40 ) (41-14)(41-28)}}$

$\sf{\implies Area = \sqrt{ 41 \times 1 \times 27 \times 13}}$

$\sf{\implies Area = \sqrt{14391}}$

$\bf{\implies \star \: Area = 119.96 \: cm^2 \: (approx) \: \star }$

❝ Hence, the area of triangle is 119.96 cm² approx. ❞

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