Lesson 8: Geometric Constructions
Madelyn had a square piece of cardboard that was 10 inches in length. She cut one 3-inch square from each corner. The shaded part represents the remaining cardboard. Show your work!
When you figure out what your question is, you can probably answer it yourself.
maybe something like shaded/total = (4*3^2)/(10-2*3)^2
As + Ac = 10*10 = 100 in^2.
As = 100 - Ac = 100 - 4*(3*3) = 64 in^2 = shaded area.
Ac = Area cut.
To solve this problem, we need to visualize the given information and then follow a series of steps to perform the necessary geometric construction. Here's how you can do it:
1. Draw a square shape with sides measuring 10 inches. This square represents the original piece of cardboard.
2. Since Madelyn cut off 3-inch squares from each corner, measure 3 inches inward from each corner along the edges of the square. Mark these points.
3. Now, draw lines connecting the marked points to form a smaller square at the center of the original square. This smaller square represents the cut-out portion.
4. Shade the area enclosed by the smaller square to represent the remaining cardboard.
Now, you have visually represented the remaining piece of cardboard as the shaded area.
To explain further, the remaining piece of cardboard can be calculated by subtracting the area of the smaller square from the area of the original square. Here's the calculation process:
The area of the original square = length * width = 10 inches * 10 inches = 100 square inches.
The area of the smaller square = side * side = 3 inches * 3 inches = 9 square inches.
Therefore, the remaining cardboard is the difference between the areas:
Remaining cardboard = Area of original square - Area of smaller square
= 100 square inches - 9 square inches
= 91 square inches.
So, the answer is that the shaded part represents 91 square inches, which is the remaining cardboard after the cut-outs.