Question

Find the area of triangle with dimension 24 24 12

Answer 1

GIVEN:

• The dimensions of a triangle are 24 cm, 24 cm, and 12 cm

TO FIND:

• What is the area of the triangle ?

SOLUTION:

Firstly, we have to find the semi perimeter of the triangle

To find the semi-perimeter of the triangle, we use the formula:-

$\large\bf{\star \: s = \dfrac{a + b + c}{2} \: \star}$

• a = 24 cm
• b = 24 cm
• c = 12 cm

According to question:

$\rm{\rightharpoonup s = \dfrac{24 + 24 + 12}{2} }$

$\rm{\rightharpoonup s = \cancel\dfrac{60}{2}}$

$\bf{\rightharpoonup \star \: s = 30 \: cm\: \star}$

To find the area of triangle, we use the Heron's formula:-

$\bf{\star \: Area = \sqrt{s(s-a)(s-b)(s-c)}\: \star}$

On putting the given values in the formula, we get

$\rm{\rightharpoonup Area = \sqrt{30(30-24)(30-24)(30-12)} }$

$\rm{\rightharpoonup Area = \sqrt{30 \times 6 \times 6 \times 18} }$

$\rm{\rightharpoonup Area = \sqrt{19440}}$

$\bf{\rightharpoonup \star \: Area = 139.42 \: cm^2\: \star}$

❝ Hence, the area of triangle is 139.42 cm² ❞

______________________

Answer 2

✬ Area = 139.32 m² ✬

Step-by-step explanation:

Given:

• Dimensions of triangle are 24 m , 24 m and 12 m. ( Let common units be meter )

To Find:

• What is the area of the triangle ?

Solution: Let ABC be a triangle where,

• AB = 24 m
• BC = 12 m
• AC = 24 m

We have to find the area of ∆ABC ,by using Heron's formula.

First finding the semi perimeter (s) of ∆.

➟ Semi perimeter = (Sum of all sides)/2

➟ S = (AB + BC + CA)/2

➟ S = (24 + 12 + 24)/2

➟ S = 60/2 = 30

★ Heron's Formula = √S ( s – a ) ( s – b ) ( s – c ) ★

➮ Ar. ∆ABC = √30(30 – 24) (30 – 12) (30 – 24) m²

➮ √30 $\times$ 6 $\times$ 18 $\times$ 6 m²

➮ √2 $\times$ 3 $\times$ 5 $\times$ 2 $\times$ 3 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 2 $\times$ 3 m²

➮ 2 $\times$ 2 $\times$ 3 $\times$ 3 √5 $\times$ 3 m²

➙ Area ∆ABC = 36√15 m²

__________________________

➱ √15 = 3.87 approx

➱ 36√15 = 36(3.87)

➱ 139.32 m²

Hence, the area of triangle is 36√15 m² or 139.32 m² (approx).