Two parallelograms have the same base length. The height of the first is half the height of the second. What is the ratio of the area of the smaller parallelogram to the area of the larger one?
A = bh
2A = 2(bh) , since the b is the same in both
area of small : area of larger = 1 : 2
Why did the parallelogram bring a measuring tape to the party? Because it wanted to measure up to the competition!
Now, let's solve this riddle. Since the base lengths of both parallelograms are the same, we can ignore them for the ratio of their areas. The ratio of the heights is given as 1:2. Since the area of a parallelogram is equal to the product of its base length and height, we can represent the ratio of their areas as (1 * 1):(2 * 2), which simplifies to 1:4.
So, the ratio of the area of the smaller parallelogram to the area of the larger one is 1:4. Just remember, even if the smaller parallelogram has a smaller area, it can still stand tall in its own way!
To find the ratio of the areas of the two parallelograms, we can use the formula for the area of a parallelogram: Area = base × height.
Let's say the base length of both parallelograms is "b", and the height of the first parallelogram is "h1" and the height of the second parallelogram is "h2". We are given that h1 = 0.5 * h2.
The area of the first parallelogram is A1 = b * h1, and the area of the second parallelogram is A2 = b * h2.
Substituting h1 = 0.5 * h2, we have A1 = b * (0.5 * h2) = 0.5 * b * h2.
Now, we can calculate the ratio of the two areas by dividing the area of the smaller parallelogram (A1) by the area of the larger parallelogram (A2):
Ratio = A1 / A2 = (0.5 * b * h2) / (b * h2).
Now, we cancel out the common factor of "b * h2" from the numerator and denominator:
Ratio = 0.5 / 1.
Therefore, the ratio of the area of the smaller parallelogram to the area of the larger one is 0.5 : 1, or simply 1 : 2.
To find the ratio of the area of the smaller parallelogram to the larger parallelogram, we need to compare their areas.
The area of a parallelogram can be calculated by multiplying its base length by its height. Let's denote the base length of both parallelograms as 'b'.
Given that the height of the first parallelogram is half the height of the second parallelogram, let's denote the height of the first parallelogram as 'h' and the height of the second parallelogram as '2h'.
Therefore, the area of the smaller parallelogram is given by A1 = b * h,
and the area of the larger parallelogram is given by A2 = b * 2h.
To find the ratio of the two areas, we divide the area of the smaller parallelogram by the area of the larger parallelogram:
Ratio = A1 / A2 = (b * h) / (b * 2h) = h / (2h) = 1/2.
Hence, the ratio of the area of the smaller parallelogram to the area of the larger parallelogram is 1/2.