Find the area of the composite figure(right triangle), where the hypotenuse is 13m, base is 12m and the height is not given?
5^2 + height^2 = 13^2
Can you please explain this to me?
recall that if the legs of a right triangle are a and b, and the hypotenuse is c, then the Pythagorean Theorem states that
a^2 + b^2 = c^2
So, the height of the triangle is 12
There are several commonly used right triangles which you would do well to commit to memory:
3-4-5
5-12-13
7-24-25
and all multiples of them, such as
6-8-10, 9-12-15, ...
To find the area of a right triangle, you can use the formula:
Area = (1/2) * base * height
In the given scenario, we know the base of the right triangle is 12m and the hypotenuse is 13m. However, the height is not provided. To find the height, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we can use this theorem to find the height of the right triangle.
Using the Pythagorean theorem:
hypotenuse^2 = base^2 + height^2
We substitute the given values:
13^2 = 12^2 + height^2
169 = 144 + height^2
Subtracting 144 from both sides:
25 = height^2
Taking the square root of both sides:
height = √25
height = 5m
Now that we have the values of the base (12m) and the height (5m), we can calculate the area using the formula mentioned earlier:
Area = (1/2) * base * height
Area = (1/2) * 12m * 5m
Area = 6m * 5m
Area = 30m^2
Therefore, the area of the given right triangle with a base of 12m and a hypotenuse of 13m is 30 square meters.