The sides of two similar trapezoids are in a ratio of 1:3. The area of the smaller trapezoid is 12 inches squared. Find the area of the larger trapezoid
To find the area of the larger trapezoid, we need to determine the ratio of their areas based on the ratio of their sides.
Let's assume that the lengths of the corresponding sides of the smaller and larger trapezoids are x and 3x, respectively.
The area of a trapezoid is given by the formula: A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the parallel sides, and h is the height.
Since the ratio of the sides is 1:3, we can write the equation for the area of the smaller trapezoid:
12 = (1/2)(x + 3x)h
Simplifying the equation, we have:
12 = (1/2)(4x)h
24 = 4xh
h = 24/4x
h = 6/x
Now, let's calculate the area of the larger trapezoid using the same formula:
A = (1/2)(b1 + b2)h = (1/2)(3x + 9x)(6/x) = (1/2)(12x)(6/x) = 72
Therefore, the area of the larger trapezoid is 72 square inches.
To find the area of the larger trapezoid, we need to use the fact that the sides of the two trapezoids are in a ratio of 1:3.
Let's assume that the lengths of the corresponding sides of the smaller trapezoid and the larger trapezoid are x and 3x, respectively.
We are given that the area of the smaller trapezoid is 12 square inches. Let's call the height of the smaller trapezoid h.
The formula to find the area of a trapezoid is: Area = (1/2) * (a + b) * h, where a and b are the lengths of the parallel sides, and h is the height.
Since we have the area and the height of the smaller trapezoid, we can substitute the values into the formula:
12 = (1/2) * (x + 3x) * h
Simplifying the equation, we have:
12 = (1/2) * 4x * h
12 = 2xh
Divide both sides of the equation by 2x to solve for h:
h = 12 / (2x)
h = 6 / x
Now that we have the height of the smaller trapezoid in terms of x, we can find the height of the larger trapezoid. Since the sides of the two trapezoids are in a ratio of 1:3, the height of the larger trapezoid, let's call it H, can be expressed as 3h:
H = 3 * h
H = 3 * (6/x)
H = 18/x
The formula to find the area of a trapezoid is: Area = (1/2) * (a + b) * h, where a and b are the lengths of the parallel sides, and h is the height.
So, the area of the larger trapezoid, A, can be calculated as:
A = (1/2) * (x + 3x) * (18/x)
A = (1/2) * 4x * (18/x)
A = (2x) * (18/x)
A = 36 square inches
Therefore, the area of the larger trapezoid is 36 square inches.
the areas of similar figures area proportional to the square of their sides
so area/12 = 3^2/1^2
area = 12(9) = 108 inches^2