What is the area in square cm of the triangle with lengths of 9cm and 7cm
To find the area of a triangle with given side lengths, you can use Heron's formula:
s = (a + b + c) / 2
area = sqrt(s * (s - a) * (s - b) * (s - c))
where a, b, and c are the side lengths and s is the semi-perimeter of the triangle.
In this case, a = 9 cm, b = 7 cm, and c is the unknown side length. To find c, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Substitute the values of a and b:
9^2 + 7^2 = c^2
81 + 49 = c^2
130 = c^2
c ≈ 11.401754
Now, calculate the semi-perimeter:
s = (9 + 7 + 11.401754) / 2
s = 13.700877
Finally, calculate the area using Heron's formula:
area = sqrt(13.700877 * (13.700877 - 9) * (13.700877 - 7) * (13.700877 - 11.401754))
area = sqrt(13.700877 * 4.700877 * 6.700877 * 2.299123)
area = sqrt(267.587657)
area ≈ 16.35 cm^2
Therefore, the area of the triangle is approximately 16.35 square cm.