To determine the area of each section of the frame, we calculated the width of the frame to be 4 cm and used that to find the area of the vertical (112 cm^2 each) and horizontal sections (160 cm^2 each). Multiplying these by 2 for each side and adding them provides a total frame area of 544 cm^2.
To find the area of each section of the frame, we first need to identify the dimensions of both the outer part of the frame and the inner part where the picture rests. According to the problem, the outer dimensions are 48 cm by 36 cm, and the inner dimensions are 40 cm by 28 cm. We're also told that the width of each section of the frame is the same all around.
To calculate the width of the frame, we can subtract the inner width from the outer width and then divide by 2 (since the frame has equal width on both sides). Doing the same for the height gives us:
Width of frame: (48 cm - 40 cm) / 2 = 4 cm
Height of frame: (36 cm - 28 cm) / 2 = 4 cm
Now, we can calculate the area of each section of the frame. The frame consists of two vertical sections and two horizontal sections, with the corners included in either the vertical or horizontal sections. The dimensions of the vertical sections are 4 cm (width of frame) by 28 cm (height of inner dimensions), and for the horizontal sections, 4 cm by 40 cm (width of inner dimensions).
Area of each vertical section: 4 cm * 28 cm = 112 cm2
Area of each horizontal section: 4 cm * 40 cm = 160 cm2
Since there are two of each type of section, we multiply these areas by 2 to find the total area covered by the frame sections:
Total area of vertical sections: 112 cm2 * 2 = 224 cm2
Total area of horizontal sections: 160 cm2 * 2 = 320 cm2
Adding these together gives us the total area of the frame: 224 cm2 + 320 cm2 = 544 cm2.