a parallelogram and a triangle both have a base of eight inches the height of a parallelogram is four inches what is the height of the triangle if both of the shapes have the same area?
a. 2 in
b. 4 in
c. 8 in
d. 10 in
Area of triangle = (1/2) * Base * Height(1)
Area of parallelogram = Base * Height(2)
If the area is same, then:
=>(1/2) * Base * Height(1) = Base * Height(2)
The Base is the same, so:
=> (1/2) * Height(1) = Height(2)
=> (1/2) * H = 4
=> H = 4*2 = 8 in
Parallelogram:
A = bh
Triangle
A = bh/2
To find the height of the triangle, we need to know the formula for the area of a parallelogram and a triangle.
The formula for the area of a parallelogram is:
Area = base * height
Given that the base of both the parallelogram and the triangle is 8 inches, and the height of the parallelogram is 4 inches, we can use this information to find the height of the triangle.
Since we want both shapes to have the same area, we can equate the area of the parallelogram to the area of the triangle:
Area of parallelogram = Area of triangle
(base of parallelogram) * (height of parallelogram) = (base of triangle) * (height of triangle)
Substituting the known values:
8 inches * 4 inches = 8 inches * (height of triangle)
32 inches^2 = 8 inches * (height of triangle)
To isolate the height of the triangle, divide both sides of the equation by 8 inches:
(height of triangle) = 32 inches^2 / 8 inches
Simplifying the expression:
(height of triangle) = 4 inches
Therefore, the height of the triangle is 4 inches.
The correct answer is b. 4 in.