Question

if A = 5cm , b=12cm ,c = 13cm what is the area of triangles abc​

Answer 1

Required Answer:-

Given:

• Sides of a triangle measures 5cm, 12cm and 13cm.

To Find:

• The area of the triangle.

Solution:

We have,

1. a = 5 cm.
2. b = 12 cm.
3. c = 13 cm.

Area of a triangle is calculated by heron's formula,

$\sf \implies A = \sqrt{s(s - a)(s - b)(s - c)}$

Where,

1. s = semi perimeter of the triangle, s = (a + b + c)/2
2. a, b and c are the sides of the triangle.

Calculate the value of s.

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

$\sf \implies s = \dfrac{5 + 12 + 13}{2}$

$\sf \implies s = \dfrac{30}{2}$

$\sf \implies s = 15$

Hence, the area of the triangle will be,

$\sf \implies A = \sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

$\sf \implies A = \sqrt{15 \times 10 \times 3 \times 2}$

$\sf \implies A = \sqrt{3 \times 5 \times 5 \times 2\times 3 \times 2}$

$\sf \implies A = \sqrt{ {(3 \times 5 \times 2)}^{2} }$

$\sf \implies A = \sqrt{ {30}^{2} }$

$\sf \implies A = 30cm^{2}$

★ Hence, the area of the triangle is 30 cm².

Answer:

• Area - 30cm²

Answer 2

$\large{ \textsf{ \textbf{ \color{royalblue}{Given \: :}}}}$

• Sides of a triangle measures 5cm, 12cm and 13cm.

$\large{ \textsf{ \textbf{ \color{royalblue}{To \: Find : }}}}$

• The area of the triangle.

$\large{ \textsf{ \textbf{ \purple{Solution \: :}}}}$

We have,

• a = 5 cm
• b = 12 cm
• c = 13 cm

Area of a triangle is calculated by heron's formula,

$\sf{ \green{ \implies A = \sqrt{s(s - a)(s - b)(s - c)}}}$

Where,

• s = semi perimeter of the triangle, s = (a + b + c)/2
• a, b and c are the sides of the triangle.

Calculate the value of s.

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

$\sf \implies s = \dfrac{5 + 12 + 13}{2}$

$\sf \implies s = \dfrac{30}{2}$

$\sf \implies {\red{s = 15}}$

Hence, the area of the triangle will be,

$\sf \implies A = \sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

$\sf \implies A = \sqrt{15 \times 10 \times 3 \times 2}$

$\sf \implies A = \sqrt{3 \times 5 \times 5 \times 2\times 3 \times 2}$

$\sf \implies A = \sqrt{ {(3 \times 5 \times 2)}^{2}}$

$\sf \implies A = \sqrt{ {30}^{2} }$

$\sf \implies{\red{ A = 30cm^{2}}}$

Hence, the area of the triangle is 30 cm².