Find the area of the triangle, whose sides are 8 cm, 10 cm, and 12 cm long. Option 1: 12√3\ cm^2 Option 2: 18√7\ cm^2 Option 3: 15√7\ cm^2 Option 4: 21√7\ cm^2

Answer: 15√7\ cm^2. Solution: Using Heron's formula with sides 8, 10, 12: semi-perimeter s = (8+10+12)/2 = 15. Area = √(s(s-a)(s-b)(s-c)) = √(15 x 7 x 5 x 3) = √1575 = √(225 x 7) = 15√7\ cm^2.

Geometry

Triangles

Medium

Find the area of the triangle, whose sides are 8 cm, 10 cm, and 12 cm long.

$12\sqrt{3}\ cm^2$

$18\sqrt{7}\ cm^2$

$15\sqrt{7}\ cm^2$

$21\sqrt{7}\ cm^2$

✅ Correct Option: 3

Using Heron's formula with sides 8, 10, 12: semi-perimeter $s = \frac{8+10+12}{2} = 15$ .

Area $= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{15 \times 7 \times 5 \times 3} = \sqrt{1575} = \sqrt{225 \times 7} = 15\sqrt{7}\ cm^2$ .

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