For an art project, you make a square print with a side length of 8 inches. You make a frame using strips of wood 1 1/4 inches wide. What is the area of the frame?
46.25
To find the area of the frame, we need to subtract the area of the inner square from the area of the outer square.
Step 1: Find the side length of the inner square.
The side length of the inner square is the length of the side of the square print minus twice the width of the frame.
Side length of the inner square = 8 inches - (2 × 1 1/4 inches)
Step 2: Simplify the expression.
Side length of the inner square = 8 inches - (2 × 5/4 inches)
= 8 inches - (10/4 inches)
= 8 inches - 2 1/2 inches
= 8 inches - 2.5 inches
= 5.5 inches
Step 3: Calculate the area of the inner square.
Area of the inner square = (Side length)^2
= (5.5 inches)^2
= 30.25 square inches
Step 4: Find the side length of the outer square.
The side length of the outer square is the length of the side of the square print plus twice the width of the frame.
Side length of the outer square = 8 inches + (2 × 1 1/4 inches)
Step 5: Simplify the expression.
Side length of the outer square = 8 inches + (2 × 5/4 inches)
= 8 inches + (10/4 inches)
= 8 inches + 2 1/2 inches
= 8 inches + 2.5 inches
= 10.5 inches
Step 6: Calculate the area of the outer square.
Area of the outer square = (Side length)^2
= (10.5 inches)^2
= 110.25 square inches
Step 7: Calculate the area of the frame.
Area of the frame = Area of the outer square - Area of the inner square
= 110.25 square inches - 30.25 square inches
= 80 square inches
Therefore, the area of the frame is 80 square inches.
To find the area of the frame, we need to first calculate the area of the outer square and then subtract the area of the inner square.
Here's how you can calculate it step by step:
Step 1: Calculate the area of the outer square.
Since the side length of the square print is 8 inches, the area of the outer square is calculated by multiplying the length of one side by itself:
Area of the outer square = 8 inches × 8 inches = 64 square inches.
Step 2: Calculate the area of the inner square.
To find the side length of the inner square, subtract twice the width of the frame from the side length of the outer square. In this case, the width of the frame is 1 1/4 inches on each side (2 sides).
Side length of the inner square = 8 inches - (1 1/4 inches + 1 1/4 inches) = 8 inches - (2 1/2 inches) = 8 inches - 2.5 inches = 5.5 inches.
The area of the inner square is calculated the same way as the outer square:
Area of the inner square = 5.5 inches × 5.5 inches = 30.25 square inches.
Step 3: Calculate the area of the frame.
To find the area of the frame, subtract the area of the inner square from the area of the outer square:
Area of the frame = Area of the outer square - Area of the inner square
= 64 square inches - 30.25 square inches
= 33.75 square inches.
Therefore, the area of the frame is 33.75 square inches.