A parallelogram and a triangle both have a base of 8 inches. the height of the parallelogram is 4 inches. what is the height of the triangle if both shapes have the same area?
area of parallelogram = base x height
area of triangle = (1/2)base x height
area of parallelogram = 8(4) in^2 = 32 in^2
32 = (1/2)(8)(height)
height = 8 inches
Well, it seems like the parallelogram and the triangle are having a competition for the same area! Let's see who wins this height challenge.
We know that the area of a parallelogram is calculated by multiplying the base and the height. So, for the parallelogram, it would be 8 (base) multiplied by 4 (height), which equals 32 square inches.
Since the triangle and the parallelogram have the same area, the height of the triangle would have to be different to compensate for its different shape. Now, let's find out how tall that triangle needs to be!
We can use the formula for the area of a triangle, which is half of the base times the height. Since we're given that the base is 8 inches, and both shapes have the same area, we know that the area of the triangle must also be 32 square inches.
Setting up an equation: (1/2) * 8 (base) * h (height) = 32.
Now let's do some math and solve for h: (1/2) * 8 * h = 32 ---> 4h = 32 ---> h = 8.
Ta-da! The height of the triangle would be 8 inches, balancing out the area competition with the parallelogram. Looks like both shapes are happy with their respective heights!
To find the height of the triangle, we need to first find the area of the parallelogram and then use that value to find the height of the triangle.
Step 1: Find the area of the parallelogram.
The area of a parallelogram is given by the formula: Area = base x height.
In this case, the base of the parallelogram is 8 inches and the height is 4 inches.
Area of the parallelogram = 8 inches x 4 inches = 32 square inches.
Step 2: Find the height of the triangle.
Since the parallelogram and the triangle have the same area, the area of the triangle will also be 32 square inches.
The area of a triangle is given by the formula: Area = (1/2) x base x height.
The base of the triangle is also given as 8 inches.
Therefore, using the formula: 32 square inches = (1/2) x 8 inches x height of the triangle.
Step 3: Solve for the height of the triangle.
Divide both sides of the equation by (1/2) x 8 inches to isolate the height of the triangle.
32 square inches / (1/2) x 8 inches = height of the triangle.
32 square inches / 4 inches = height of the triangle.
8 inches = height of the triangle.
Therefore, the height of the triangle is 8 inches.
To find the height of the triangle, we need to compare the areas of the parallelogram and the triangle since they have equal areas.
First, let's find the area of the parallelogram. The formula for the area of a parallelogram is given by:
Area = base x height
In this case, the base of the parallelogram is 8 inches, and the height is 4 inches. Plugging these values into the formula:
Area of parallelogram = 8 inches x 4 inches = 32 square inches
Since the triangle and the parallelogram have equal areas, the area of the triangle is also 32 square inches.
The formula for the area of a triangle is given by:
Area = (base x height) / 2
The base of the triangle is also 8 inches, and we need to find the height. Rearranging the formula to solve for height:
Height = (2 x Area) / base
Substituting the known values:
Height = (2 x 32 square inches) / 8 inches
Height = 64 square inches / 8 inches
Simplifying the expression:
Height = 8 inches
Therefore, the height of the triangle is 8 inches.