32: The trapezoids are similar. The area of the smaller trapezoid is 711 m².
Find the area of the larger trapezoid to the nearest whole number.
The one trapezoid has a base of 27 m and the larger one has a base of 39 m.
39: Find the circumference. Leave your answer in terms of π.
It is a circle with a radius of 18 inches.
(multiple choice)
A. 36π in.
B. 324π in.
C. 18π in.
D. 54π in.
Since the shapes are similar, their areas are proportional to the square of their corresponding sides, so
area-of-larger/711 = 39^2/27^2
solve
For the second one, surely you know that the perimeter of a circle is 2πr.
32: To find the area of the larger trapezoid, we can use the principle of similar figures. The ratio of the lengths of the bases of the two trapezoids is 39/27 = 13/9. Since the area is a two-dimensional measurement, it is proportional to the square of the length. Therefore, the ratio of the areas of the two trapezoids is (13/9)^2.
Given that the area of the smaller trapezoid is 711 m², we can set up the following equation:
Area of larger trapezoid / Area of smaller trapezoid = (13/9)^2
Let's solve for the area of the larger trapezoid:
Area of larger trapezoid = Area of smaller trapezoid * (13/9)^2
= 711 * (13/9)^2
≈ 1452
Therefore, the area of the larger trapezoid to the nearest whole number is 1452 m².
39: To find the circumference of a circle, we can use the formula:
Circumference = 2 * π * radius
Given that the radius of the circle is 18 inches, we can substitute the value into the formula:
Circumference = 2 * π * 18 inches
= 36π inches
Therefore, the circumference of the circle is 36π inches, which is option A. 36π in.
1. To find the area of the larger trapezoid, we can use the concept of similarity. Since the trapezoids are similar, their corresponding sides are proportional.
The formula for the area of a trapezoid is (1/2) * (base1 + base2) * height.
Let's denote the height of the smaller trapezoid as h1 and its area as A1, and the height of the larger trapezoid as h2 and its area as A2.
We have the following proportions:
h1 / h2 = base1 / base2
Substituting the given values:
h1 / h2 = 27 / 39
To find the area of the larger trapezoid, we can use the formula:
A2 = A1 * (base2 / base1) * (h2 / h1)
Now, plug in the values:
A1 = 711 m²
base1 = 27 m
base2 = 39 m
h1 / h2 = 27 / 39
A2 = 711 * (39 / 27) * (27 / 39)
Simplifying the expression, canceling out common factors:
A2 = 711 * 3/2
A2 = 1066.5 m²
Rounding to the nearest whole number, the area of the larger trapezoid is approximately 1067 m².
2. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Given that the radius of the circle is 18 inches, we can calculate the circumference using the formula:
C = 2π * 18 in
C = 36π in
Therefore, the circumference of the circle is 36π inches.