A triangle has sides measuring 5 cm, 12 cm, and 13 cm. What is its area?

A triangle has sides measuring 5 cm, 12 cm, and 13 cm. What is its area?

• A. 30 cm²
• B. 40 cm²
• C. 50 cm²
• D. 60 cm²

Answer: (A)

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. First, calculate the semi-perimeter \(s\) of the triangle, which is the sum of the lengths of its sides divided by 2: \[ s = \frac{a + b + c}{2} = \frac{5 + 12 + 13}{2} = 15 \, \text{cm} \] Next, you apply Heron's formula, which is: \[ Area = \sqrt{s(s-a)(s-b)(s-c)} \] Now substituting in our values, where \(a = 5\) cm, \(b = 12\) cm, and \(c = 13\) cm: \[ Area = \sqrt{15(15-5)(15-12)(15-13)} \] Calculating each term inside the square root: \[ Area = \sqrt{15 \times 10 \times 3 \times 2} = \sqrt{15 \times 60} = \sqrt{900} = 30 \, \text{cm}^2 \] Thus, the area of the

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. First, calculate the semi-perimeter (s) of the triangle, which is the sum of the lengths of its sides divided by 2:

[

s = \frac{a + b + c}{2} = \frac{5 + 12 + 13}{2} = 15 , \text{cm}

]

Next, you apply Heron's formula, which is:

[

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

]

Now substituting in our values, where (a = 5) cm, (b = 12) cm, and (c = 13) cm:

[

Area = \sqrt{15(15-5)(15-12)(15-13)}

]

Calculating each term inside the square root:

[

Area = \sqrt{15 \times 10 \times 3 \times 2} = \sqrt{15 \times 60} = \sqrt{900} = 30 , \text{cm}^2

]

Thus, the area of the