Area of isosceles tringle if base is 6 cm and perimeter is 26 cm
I don't know how the army does this. Trig? formula.
The formula using straight algebra is
A = sqrt(p(p-a)(p-b)(p-c) where
p is 1/2 the perimeter and a,b,c are the sides.
The perimeter is 26 and the base is 6 which makes the other two sides 26-6 = 20 and since it is an isosceles triangle the other two sides must be 10 each.
A in cm^2 = sqrt[13(13-10)(13-10)(13-6)]
let each of the equal sides be x
2x + 6 = 26
x = 10
make a sketch of the triangle, draw in its height h
h^2 + 3^2 = 10^2
h = √91
area = (1/2)(6)√91 = 3√91 cm^2
which is the same as DrBob's answer
To find the area of an isosceles triangle, we need to know either the height or the length of the two equal sides. However, in this case, only the base and perimeter of the triangle are provided.
To find the missing information, we can use the given perimeter of 26 cm. Remember that in an isosceles triangle, the two equal sides have the same length. Since the perimeter is the sum of all three sides, and we know the base is 6 cm, we can find the length of the two equal sides by subtracting the base from the perimeter, and then divide the result by 2.
Let's calculate it step by step:
Step 1: Subtract the base from the perimeter:
Perimeter - Base = 26 cm - 6 cm = 20 cm
Step 2: Divide the result by 2 to find the length of the two equal sides:
20 cm ÷ 2 = 10 cm
Now we have the length of the two equal sides, but we still need the height to calculate the area. Unfortunately, the height is not provided in the question.
Therefore, we cannot determine the exact area of the isosceles triangle without the height. The area of a triangle is calculated using the formula: Area = (base × height) / 2.
If you are given the height of the isosceles triangle, you can substitute it into the formula along with the given base to find the area.