Question

Find the area of a triangle, whose sides are 0.24 m, 28 cm and 32 cm.

• A. 84\sqrt{15}$ $cm^2
• B. 82\sqrt{15}$ $cm^2
• C. 86\sqrt{15}$ $cm^2
• D. 88\sqrt{15}$ $cm^2

Answer 1

Answer:

84\sqrt{15}$ $cm^2

the area of a triangle with sides a, b, and c is given by:

Area = $\sqrt{(s × (s - a) × (s - b) × (s - c))}$

where s is the semi-perimeter of the triangle:

$s = (a + b + c) / 2$

Inserting our values:

$s = (24 + 28 + 32) / 2 = 42$

$Area = \sqrt{(42 × (42 - 24) × (42 - 28) × (42 - 32))}$

$Area = \sqrt{(42 × 18 × 14 × 10)}$

$Area = \sqrt{105840}$

We recognize that the expression can be rewritten to include a perfect square:

$Area = \sqrt{(15 × 7056)}$

$Area = 84\sqrt{15}$ cm²