Find the area of the triangle with the length of the side 9CM 10 cm an

1.	Find the area of the triangle with the length of the side 9CM 10 cm and 17 cm
Answer» AREA of TRIANGLE is 36 cm². Step-by-step explanation : To find :- Area of triangle. Solution:- Given, Sides of triangle are 9 cm, 10cm and 17 cm. We USE Heron's formula for finding area of triangle because HEIGHT of triangle is not given. Heron's formula is : $\sf \bold{ Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} }$ Where, s is semi-perimeter of triangle. a, b and c are sides of triangle. So, $\sf Semi - perimeter_{(Triangle)} = \dfrac{Perimeter}{2} \\ \\ \sf Semi - permeter_{(Triangle)} = \dfrac{36}{2} \\ \\ \sf \blue{Semi - perimter_{(Triangle)} = \bold{18}}$ Semi-perimeter of triangle is 18 cm. Now, $\sf \longrightarrow Area_{(Triangle)} = \sqrt{18 \times (18 - 9)(18 - 10)(18 - 17)}$ $\sf \longrightarrow Area_{(Triangle)} = \sqrt{18 \times 9 \times 8 \times 1}$ $\sf \longrightarrow Area_{(Triangle)} = \sqrt{2 \times 3 \times 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 1}$ $\sf \longrightarrow Area_{(Triangle)} = 2 \times 2 \times 3 \times 3 \times 1$ $\sf \longrightarrow \purple{\boxed{\sf \bold{Area_{(Triangle)} = 36}} \bigstar}$ THEREFORE, Area of triangle is 36 cm².

Find the area of the triangle with the length of the side 9CM 10 cm and 17 cm

Answer»

AREA of TRIANGLE is 36 cm².

Step-by-step explanation :

To find :-

Area of triangle.

Solution:-

Given,

Sides of triangle are 9 cm, 10cm and 17 cm.

We USE Heron's formula for finding area of triangle because HEIGHT of triangle is not given.

Heron's formula is :

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

Where,

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

So,

$\sf Semi - perimeter_{(Triangle)} = \dfrac{Perimeter}{2} \\ \\ \sf Semi - permeter_{(Triangle)} = \dfrac{36}{2} \\ \\ \sf \blue{Semi - perimter_{(Triangle)} = \bold{18}}$