a square photograph measuring 8 inches by 8 inches is positioned within a 1 inch wide picture frame as best shown. select the best answer.
what is the combined area of the photograph and frame?
left and right sides of frame = 1 + 1 = 2 in
top and bottom sides of frame = 1 + 1 = 2 in
therefore the total length and width are:
L = 8 + 2 = 10 in
W = 8 + 2 = 10 in
recall that area of rectangle is given by
A = L*W
A = 10*10
A = 100 in^2
hope this helps~ :)
Awesome!!
To find the combined area of the photograph and frame, we need to first calculate the area of the photograph and then add it to the area of the frame.
The area of the photograph is calculated by multiplying its length by its width, which is 8 inches by 8 inches:
Area of photograph = length × width = 8 inches × 8 inches = 64 square inches.
The frame is 1 inch wide around the photograph, so to calculate its area, we need to add 1 inch to each side of the photograph's dimensions:
Length of frame = length of photograph + (2 × width of frame) = 8 inches + (2 × 1 inch) = 8 inches + 2 inches = 10 inches.
Width of frame = width of photograph + (2 × width of frame) = 8 inches + (2 × 1 inch) = 8 inches + 2 inches = 10 inches.
Area of frame = length of frame × width of frame = 10 inches × 10 inches = 100 square inches.
Finally, to find the combined area of the photograph and frame, we add the area of the photograph to the area of the frame:
Combined area = Area of photograph + Area of frame = 64 square inches + 100 square inches = 164 square inches.
Therefore, the combined area of the photograph and frame is 164 square inches.
To find the combined area of the photograph and frame, we first need to find the area of the photograph and then add the area of the frame.
The area of the photograph is calculated by multiplying its length by its width. In this case, the photograph is a square measuring 8 inches by 8 inches, so the area of the photograph is:
Area of the photograph = Length of the photograph x Width of the photograph = 8 inches x 8 inches = 64 square inches.
Now, let's calculate the area of the frame. The frame is 1 inch wide on all sides, so it forms an outer square around the photograph. To find the area of the frame, we need to calculate the difference between the area of the outer square and the area of the inner square (photograph). The outer square has side length 8 + 2(1) = 10 inches (adding the frame width on both sides).
Area of the frame = Area of the outer square - Area of the inner square
= (Side length of the outer square)^2 - (Side length of the inner square)^2
= (10 inches)^2 - (8 inches)^2
= 100 square inches - 64 square inches
= 36 square inches.
Finally, to find the combined area of the photograph and frame, we add the area of the photograph to the area of the frame:
Combined area = Area of the photograph + Area of the frame
= 64 square inches + 36 square inches
= 100 square inches.
Therefore, the combined area of the photograph and frame is 100 square inches.