Question

13. Find the area of the triangle in which
(1) a =13 m.b=14 m.c=15 m:​

Answer 1

ATQ:

a = 13m

b = 14m

c = 15m.

Since we've been given the sides of the triangle, we can find the area of the triangle by using the Heron's Formula.

We first need to find the semi-perimeter (s).

$\Longrightarrow \sf s = \dfrac{a + b + c}{2}$

$\Longrightarrow \sf s = \dfrac{13 + 14 + 15}{2}$

$\Longrightarrow \sf s = \dfrac{42}{2}$

$\Longrightarrow \sf s = 21m$

By using Heron's Formula we get;

$\Longrightarrow \sf \triangle ABC = \sqrt{s(s-a) (s-b) (s-c)}$

$\Longrightarrow \sf \triangle ABC = \sqrt{21 \ (21-13) \ (21-14) \ (21-15)}$

$\Longrightarrow \sf \triangle ABC = \sqrt{21 \ (8) \ (7) \ (6)}$

$\Longrightarrow \sf \triangle ABC = \sqrt{ (7 \times 3) \ (2 \times 2 \times 2) \ (7) \ (2 \times 3)}$

$\Longrightarrow \sf \triangle ABC = \sqrt{7 \times 3 \times 2 \times 2 \times 2 \times 7 \times 2 \times 3}$

$\Longrightarrow \sf \triangle ABC = \sqrt{7 \times 7 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2}$

$\Longrightarrow \sf \triangle ABC = \sqrt{7^2 \times 3^2 \times 2^2 \times 2^2}$

$\Longrightarrow \sf \triangle ABC = 7 \times 3 \times 2 \times 2$

$\Longrightarrow \underline{\underline{\bf{\triangle ABC = 84 m^2}}}$

Therefore the area of the triangle with the sides 13m, 14m & 15m will be 84m².

Answer 2

Question:-

➣ Find the Area of the Triangle:-

AnSwEr:-

➣

• Given:-

➣ a = 13m

➣ b = 14m

➣ c = 15m

• To Find:-

➣ Area of the Triangle with the given sides

• We know:-

➣ Heron's Formula = $\\ \sqrt{s(s-a) (s-b) (s-c)}$

• Soln:-

➣

• Firstly finding the Semi- Perimeter(s):-

$s = \dfrac{a + b + c}{2}$

$s = \dfrac{13 + 14 + 15}{2}$

$s = \dfrac{42}{2}$

$s = \cancel{\dfrac{42}{2}}$

$\bf{s = 21m}$

➣ Using Heron's Formula:-

$\triangle ABC = \sqrt{s(s-a) (s-b) (s-c)}$

$\triangle ABC = \sqrt{21 \ (21-13) \ (21-14) \ (21-15)}$

$\triangle ABC = \sqrt{21 \ (8) \ (7) \ (6)}$

$\triangle ABC = \sqrt{ (7 \times 3) \ (2 \times 2 \times 2) \ (7) \ (2 \times 3)}$

$\triangle ABC = \sqrt{7 \times 3 \times 2 \times 2 \times 2 \times 7 \times 2 \times 3}$

$\triangle ABC = \sqrt{7 \times 7 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2}$

$\triangle ABC = \sqrt{7^2 \times 3^2 \times 2^2 \times 2^2}$

$\triangle ABC = 7 \times 3 \times 2 \times 2$

$\bf{\triangle ABC = 84 m^2}$

➣Hence, we find out that the Area of the Triangle with the given sides will be 84m²

•Recalling the Formulas Used:-

➣ Formula of Semi-Perimeter= $\bf{s = \dfrac{a + b + c}{2}}$

➣Heron's Formula = $\\ \sqrt{s(s-a) (s-b) (s-c)}$