Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm.

1.	Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also, find the height corresponding to the smallest side.
Answer» Let a, b and c be the sides of a triangle. Apply Heron's Formula to find the area of triangle. Area = \(\sqrt{S(S-a)(S-b)(S-c)}\) Where S = \(\frac{a + b + c}{2}\) Here a = 18 cm, b = 24 cm, c = 30 cm Now, S = 1/2(18+24+30) = 36 Area = √(36(36-18)(36-24)(36-30)) = √(36 × 18× 12 × 6) = 216 Area is 216 cm² From given, Length of smallest side = 18 cm Area of a triangle = 1/2 × Base × Height 216 = 1/2 x 18 x height Height = 24 Therefore, the height corresponding to the smallest side is 24 cm.

Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also, find the height corresponding to the smallest side.

Answer»

Let a, b and c be the sides of a triangle.

Apply Heron's Formula to find the area of triangle.

Area = \(\sqrt{S(S-a)(S-b)(S-c)}\)

Where S = \(\frac{a + b + c}{2}\)

Here a = 18 cm, b = 24 cm, c = 30 cm

Now,

S = 1/2(18+24+30) = 36

Area = √(36(36-18)(36-24)(36-30))

= √(36 × 18× 12 × 6)

= 216

Area is 216 cm²

From given, Length of smallest side = 18 cm

Area of a triangle = 1/2 × Base × Height

216 = 1/2 x 18 x height

Height = 24

Therefore, the height corresponding to the smallest side is 24 cm.