Question

What is the area of a triangle whose sides are 12, 12 and 6. Using herons formula

Answer 1

✦ Question :-

What is the area of a triangle whose sides are 12, 12 and 6.

✦ Answer :-

Area of Triangle is 9√15cm²

✦ Given :-

Sides of the Triangle = 12 , 12 and 6.

✦ To Find:-

Area of Triangle = ?

✦ Solution :-

Let's find out Semi perimeter :-

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

✦ s = ( 12 + 12 + 6)/2

✦ s = 30/2

✦ s = 15 units.

Now,

Area of Triangle = √[ s ( s-a) (s-b) (s-c) ]

↠ Area = √[ 15 ( 15 -12)(15-12)(15-6) ]

↠ Area = √[ 15 × 3 × 3 × 9 ]

↠ Area = √15×3×3×9

↠ Area = √5×3×3×3×3×3

↠ Area = 3×3√5×3

↠ Area = 9√15cm²

↠ Area = 9√15cm² .

Hence,

Area of Triangle is 9√15cm²

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .

Answer 2

☆ Solution ☆

Given

• Sides are 12, 12 and 6

To find

• Area of triangle using herons formula.

Step-by-Step-Explaination

According to given question :

As we know that herons formula

$= > \: s = \frac{a + b + c}{2}$

$= > \: s = \frac{12 + 12 + 6}{2}$

$= > \: s = \frac{30}{2}$

$= > \: s = 15$

Area of Triangle = $\sqrt{s \: (s - a) \:(s - b) \: (s - c) }$

Area of Triangle = $\sqrt{15 \: (15- 12) \:(15 - 12) \: (15 - 6) }$

Area of Triangle = $\sqrt{15 \times 3 \times 3 \times 9}$

Area of Triangle = $\sqrt{1215}$

Area of Traingle = 34.85685

Hence,

Area of Triangle is 34.85685.