The base of a pyramid is 10 cm high is the triangle shown. Find the volume of the pyramid. The hieght/leg of the traingle is 4 the base/leg is 6 and the hypothnues is 7.21
The first sentence makes no sense. The second sentence doesn't help.
V = Ab*h/3. Ab = area of base.
Ab = 10cm * 6cm = 60cm^2,
V = 60cm^2 * 4cm /3 = 80cm^3.
To find the volume of a pyramid, you need to know the base area and the height of the pyramid. In this case, the base is a triangle, so we'll first find the area of the triangle.
Given that the height of the triangle is 4 cm, the base is 6 cm, and the hypotenuse is 7.21 cm, we can use the Pythagorean theorem to find the other two sides of the triangle.
According to the Pythagorean theorem, the square of the hypotenuse (7.21) is equal to the sum of the squares of the other two sides.
Let's call the two sides A and B. So, we have A^2 + B^2 = 7.21^2.
The base of the triangle is given as 6 cm, which is one of the sides, so let's assume that 6 cm is Side B.
So, we have B^2 + 4^2 = 7.21^2.
Simplifying further, we have 36 + 16 = 52.1441.
Therefore, B^2 = 52.1441 - 36.
B^2 = 16.1441.
Taking the square root of both sides, we get B = 4.02 cm.
Now we have the two sides of the triangle. The base (leg) is 6 cm, and the other leg is 4.02 cm.
To find the area of the triangle, we'll use the formula for the area of a triangle: A = (1/2) * base * height.
Substituting the values, we have A = (1/2) * 6 * 4.02.
Simplifying further, we get A = 12.06 cm^2.
So, the base area of the pyramid is 12.06 cm^2.
Finally, to find the volume of the pyramid, we'll use the formula: volume = (1/3) * base area * height.
Substituting the values, we have volume = (1/3) * 12.06 * 10.
Simplifying further, we get volume = 40.2 cm^3.
Therefore, the volume of the pyramid is 40.2 cm^3.