To find the area of a triangle using Heron's formula, you first need to calculate the semi-perimeter (\(s\)) of the triangle. The semi-perimeter is half of the perimeter. In this case, the perimeter is 42 cm, so \(s = \frac{42}{2} = 21\) cm.
Next, you can use Heron's formula to find the area (\(A\)) of the triangle. Heron's formula states that for a triangle with sides of lengths \(a\), \(b\), and \(c\), and semi-perimeter \(s\), the area \(A\) is given by:
\[A = \sqrt{s(s - a)(s - b)(s - c)}\]
In this problem, the sides are given as 18 cm and 10 cm, and the semi-perimeter is 21 cm. Substituting these values into the formula:
\[A = \sqrt{21(21 - 18)(21 - 10)(21 - 18)}\]
\[A = \sqrt{21 \times 3 \times 11 \times 3}\]
\[A = \sqrt{2079}\]
Using a calculator, find the square root of 2079, which is approximately \(45.57\) cm² (rounded to two decimal places).
Therefore, the area of the triangle is approximately \(45.57\) cm².
Answers & Comments
Answer:
To find the area of a triangle using Heron's formula, you first need to calculate the semi-perimeter (\(s\)) of the triangle. The semi-perimeter is half of the perimeter. In this case, the perimeter is 42 cm, so \(s = \frac{42}{2} = 21\) cm.
Next, you can use Heron's formula to find the area (\(A\)) of the triangle. Heron's formula states that for a triangle with sides of lengths \(a\), \(b\), and \(c\), and semi-perimeter \(s\), the area \(A\) is given by:
\[A = \sqrt{s(s - a)(s - b)(s - c)}\]
In this problem, the sides are given as 18 cm and 10 cm, and the semi-perimeter is 21 cm. Substituting these values into the formula:
\[A = \sqrt{21(21 - 18)(21 - 10)(21 - 18)}\]
\[A = \sqrt{21 \times 3 \times 11 \times 3}\]
\[A = \sqrt{2079}\]
Using a calculator, find the square root of 2079, which is approximately \(45.57\) cm² (rounded to two decimal places).
Therefore, the area of the triangle is approximately \(45.57\) cm².
Answer:
42-(18+10)
42-28=14 cm