A picture is 42 cm long and 32 cm wide. It has a 5 cm frame around it.all around the picture, 1 cm of the picture sticks into the frame so that the frame can hold it. What is the area of the frame?
Plz help
Interpretation: I will see 4 cm of framing all around.
Add 4 cm to each end of the width ---> width of frame = 32+8 = 40 cm
length of frame = .....
area = length x width = ....
To find the area of the frame, we need to calculate the difference between the area of the outer rectangle (including the frame) and the area of the inner rectangle (just the picture).
First, let's calculate the area of the outer rectangle. We know that the length of the outer rectangle is the length of the picture plus twice the width of the frame since there are two vertical sides of the frame. Similarly, the width of the outer rectangle is the width of the picture plus twice the width of the frame since there are two horizontal sides of the frame.
Length of outer rectangle = length of picture + 2 * width of frame
Width of outer rectangle = width of picture + 2 * width of frame
Given:
Length of picture = 42 cm
Width of picture = 32 cm
Width of frame = 1 cm
Length of outer rectangle = 42 cm + 2 * 1 cm = 42 cm + 2 cm = 44 cm
Width of outer rectangle = 32 cm + 2 * 1 cm = 32 cm + 2 cm = 34 cm
Now, let's calculate the area of the outer rectangle:
Area of outer rectangle = Length of outer rectangle * Width of outer rectangle
= 44 cm * 34 cm
= 1496 cm²
Next, we need to calculate the area of the inner rectangle. Since 1 cm of the picture sticks into the frame around all four sides, we need to subtract this extra 1 cm from both the length and width of the picture.
Length of inner rectangle = Length of picture - 2 * width of frame
Width of inner rectangle = Width of picture - 2 * width of frame
Length of inner rectangle = 42 cm - 2 * 1 cm = 42 cm - 2 cm = 40 cm
Width of inner rectangle = 32 cm - 2 * 1 cm = 32 cm - 2 cm = 30 cm
Now, let's calculate the area of the inner rectangle:
Area of inner rectangle = Length of inner rectangle * Width of inner rectangle
= 40 cm * 30 cm
= 1200 cm²
Finally, we can find the area of the frame by subtracting the area of the inner rectangle from the area of the outer rectangle:
Area of frame = Area of outer rectangle - Area of inner rectangle
= 1496 cm² - 1200 cm²
= 296 cm²
Therefore, the area of the frame is 296 cm².