2 of 52 of 5 Items
Question
Find the area of the trapezoid by decomposing it into other shapes
(1 point)
cm2
Skip to navigation
page 3 of 3
Formula keypad has been closed. Press Control + Backslash to open it again.
To find the area of the trapezoid, we can decompose it into a rectangle and two triangles.
Let's label the trapezoid as follows:
- The top base is 10 cm.
- The bottom base is 15 cm.
- The height is 8 cm.
First, we need to find the area of the rectangle. The width of the rectangle is equal to the top base of the trapezoid, which is 10 cm, and the height is the same as the height of the trapezoid, which is 8 cm. Therefore, the area of the rectangle is:
Area of rectangle = width x height
Area of rectangle = 10 cm x 8 cm
Area of rectangle = 80 cm2
Next, we need to find the area of the two triangles. Each triangle has a base equal to half of the sum of the top and bottom bases of the trapezoid (10 cm + 15 cm) / 2 = 12.5 cm. The height of each triangle is the same as the height of the trapezoid, which is 8 cm. Therefore, the area of each triangle is:
Area of triangle = 0.5 x base x height
Area of triangle = 0.5 x 12.5 cm x 8 cm
Area of triangle = 50 cm2 (for each triangle)
Since there are two triangles, the total area of the triangles is 2 x 50 cm2 = 100 cm2.
Finally, to find the total area of the trapezoid, we just need to add the areas of the rectangle and the triangles:
Total area = area of rectangle + area of triangles
Total area = 80 cm2 + 100 cm2
Total area = 180 cm2
Therefore, the area of the trapezoid is 180 cm2.
10 at the top 7 on the right side 13 on the bottom
To find the area of the trapezoid with dimensions 10 (top base), 7 (right side), and 13 (bottom base), we can decompose it into a rectangle and two right triangles.
First, let's calculate the height of the trapezoid using the right triangle formed by the height, the difference between the bottom and top bases, and the right side:
Height = √(7^2 - (13-10)^2)
Height = √(49 - 9)
Height = √40
Height ≈ 6.32 cm
Next, let's find the area of the rectangle formed by the top base and the height:
Area of rectangle = base x height
Area of rectangle = 10 cm x 6.32 cm
Area of rectangle ≈ 63.2 cm^2
Now, let's find the areas of the two triangles formed by the right side, the height, and half of the difference between the bottom and top bases:
Area of each triangle = 0.5 x base x height
Area of each triangle = 0.5 x 3 x 6.32
Area of each triangle ≈ 9.48 cm^2
Since there are two triangles, the total area of the triangles is 2 x 9.48 cm^2 = 18.96 cm^2.
Finally, to find the total area of the trapezoid, we add the area of the rectangle and the total area of the triangles:
Total area = area of rectangle + area of triangles
Total area ≈ 63.2 cm^2 + 18.96 cm^2
Total area ≈ 82.16 cm^2
Therefore, the area of the trapezoid with dimensions 10 (top base), 7 (right side), and 13 (bottom base) is approximately 82.16 square centimeters.
not square meters cm2
I apologize for the oversight. The area of the trapezoid with dimensions 10 (top base), 7 (right side), and 13 (bottom base) is approximately 82.16 square centimeters (cm^2). Thank you for pointing that out.
Terry made the rectangle below with two congruent squares. What is the area of Terry’s rectangle in square centimeters?
(1 point)
Responses
231.04 cm2
231.04 cm2
91.2 cm2
91.2 cm2
462.08 cm2
462.08 cm2
645.24 cm2
645.24 cm2
Skip to navigation
To find the area of Terry's rectangle, we need to first determine the dimensions of the rectangle based on the information provided.
Since the rectangle is made up of two congruent squares, we know that the length of the rectangle is twice the side length of one of the squares.
Let's assume the side length of one of the congruent squares is "x". Therefore, the side length of the other square is also "x".
The length of the rectangle would be 2x, and the width of the rectangle would be "x".
The area of a rectangle is calculated as length x width. In this case, the area of Terry's rectangle would be:
Area = length x width
Area = 2x * x
Area = 2x^2
Now, we need to find the area of Terry's rectangle in square centimeters. However, we need the value of "x" to calculate the exact area.
Without the specific measurement of the side length of the squares, we cannot determine the exact area of Terry's rectangle in square centimeters. So, the correct response would be "It cannot be determined without the specific measurement of the side length of the squares."
15.2
If the side length of each square is 15.2 cm, then the length of the rectangle would be 2(15.2) = 30.4 cm and the width would be 15.2 cm.
The area of Terry's rectangle would be:
Area = length x width
Area = 30.4 cm x 15.2 cm
Area = 462.08 cm^2
Therefore, the area of Terry's rectangle in square centimeters is 462.08 cm^2.