Question

the sides of a right triangle are 5cm,,12cmand13cm .then the area is​

Answer 1

Step - by - Step - Explanation

Assume that ,

ABC be a Right triangle.

Where,

• AB = 5 cm
• BC = 12 cm
• CA = 13 cm

Formula Method.

★ Area of right triangle = 1/2 × base × height

Here,

• Base = AB = 5 cm
• Height = BC = 12 cm

So, keep all values,

➡ Area of right triangle ABC = 1/2 × 5 × 12

➡ Area of right triangle ABC = 5 × 6

➡ Area of right triangle ABC = 30 cm²

_________________________

Using Heron's Formula

Let,

➡Semi perimeter (S) = (AB + BC + CA)/2

So,

➡ Semi perimeter (S) = (5+12+13)/2

➡ Semi perimeter (S) = 30/2

➡ Semi perimeter (S) = 15 cm

Heron's Formula,

★Area = √[S(S-AB)(S-BC)(S-CA)]

keep all above values

➡ Area = √[15(15-5)(15-12)(15-13)]

➡Area = √[15×10×3×2]

➡Area = √(900)

➡Area = 30 cm²

_________________________

Hence

• Area of right triangle will be = 30cm²

________________

Answer 2

Solution :

We have the sides of a right angled triangle are 5 cm, 12 cm & 13 cm.

$\underline{\bf{Explanation\::}}}$

Attachment a diagram of right triangle according to the given question;

Where as;

• Perpendicular, (AB)  = 5 cm
• Base, (BC) = 12 cm
• Hypotenuse, (AC) = 13 cm

We know that formula of the area of triangle :

$\boxed{\bf{Area \:of\:\triangle = \frac{1}{2} \times base\times height }}}$

$\longrightarrow\sf{Area\:of\:\triangle = \dfrac{1}{2} \times Base \times Height }\\ \\ \longrightarrow\sf{Area\:of\:\triangle = \dfrac{1}{2} \times BC \times AB }\\\\\longrightarrow\sf{Area\:of\:\triangle = \dfrac{1}{\cancel{2}} \times \cancel{12} \times 5}\\\\\longrightarrow\sf{Area\:of\:\triangle = 6\times 5}\\\\\longrightarrow\bf{Area\:of\:\triangle = 30\:cm^{2} }$

Thus;

The area of triangle will be 30 cm² .