Compute the area of a triangle with sides.
15 × 15 × 18
a = How many square units?
There is a formula for the area of a triangle in terms of the side lengths.
Don't ask me to derive it. Here it is:
Let s = (a +b +c)/2
a,b and c are the side lengths.
For your triangle, s = 24
Area = sqrt[s*(s-a)*(s-b)*(s-c)]
= sqrt[24*9*9*6) = 108 square units
Check: Your triangle is isosceles and if you drop a line from the apex to the middle of the base, you have two
9:12:15 right triangles. The area of each is (1/2)(9*12) and that makes a total area of 108.
To compute the area of a triangle with sides 15, 15, and 18, you can use Heron's formula:
1. First, calculate the semi-perimeter of the triangle, denoted by "s". The semi-perimeter is the sum of all the sides divided by 2. In this case, it would be s = (15 + 15 + 18) / 2 = 24.
2. Then, use Heron's formula to calculate the area ("A") of the triangle:
A = sqrt(s * (s - side1) * (s - side2) * (s - side3))
Plugging in the values, we have:
A = sqrt(24 * (24 - 15) * (24 - 15) * (24 - 18))
Now, let's calculate the area step by step:
A = sqrt(24 * 9 * 9 * 6)
A = sqrt(1944)
A = 44.09 (rounded to two decimal places)
So, the area of the triangle with sides 15, 15, and 18 is approximately 44.09 square units.
To compute the area of a triangle with sides 15, 15, and 18, you can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:
area = √(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle and is calculated as:
s = (a + b + c) / 2
In this case, the sides are 15, 15, and 18. Let's substitute these values into the formula:
s = (15 + 15 + 18) / 2
s = 48 / 2
s = 24
Now, we can calculate the area using Heron's formula:
area = √(24 * (24 - 15) * (24 - 15) * (24 - 18))
area = √(24 * 9 * 9 * 6)
area = √(11664)
area ≈ 108.05
Therefore, the area of the triangle with sides 15, 15, and 18 is approximately 108.05 square units.