a rectangle picture measures 12 cm by 30 cm. it is mounted in a frame 2 cm wide. fin the area of the frame.

it is Area outside-area inside= 16x34-12x30

184

To find the area of the frame, we need to subtract the area of the rectangle from the area of the larger rectangle formed by the frame.

1. Find the area of the rectangle:
Area of rectangle = Length x Width
Area of rectangle = 12 cm x 30 cm
Area of rectangle = 360 cm²

2. Find the dimensions of the larger rectangle formed by the frame:
Length of larger rectangle = Length of rectangle + 2 times the frame width
Length of larger rectangle = 12 cm + 2 cm + 2 cm
Length of larger rectangle = 16 cm

Width of larger rectangle = Width of rectangle + 2 times the frame width
Width of larger rectangle = 30 cm + 2 cm + 2 cm
Width of larger rectangle = 34 cm

3. Find the area of the larger rectangle:
Area of larger rectangle = Length x Width
Area of larger rectangle = 16 cm x 34 cm
Area of larger rectangle = 544 cm²

4. Find the area of the frame by subtracting the area of the rectangle from the area of the larger rectangle:
Area of frame = Area of larger rectangle - Area of rectangle
Area of frame = 544 cm² - 360 cm²
Area of frame = 184 cm²

Therefore, the area of the frame is 184 cm².

To find the area of the frame around the rectangle picture, we need to subtract the area of the picture from the area of the rectangle formed by the frame.

The dimensions of the picture are given as 12 cm by 30 cm, and the frame is 2 cm wide. This means that the dimensions of the rectangle formed by the frame are: length = (12 + 2 + 2) cm and width = (30 + 2 + 2) cm.

Calculating the dimensions of the rectangle formed by the frame:
Length of frame = length of picture + 2 * width of frame = 12 cm + 2 * 2 cm = 12 cm + 4 cm = 16 cm
Width of frame = width of picture + 2 * width of frame = 30 cm + 2 * 2 cm = 30 cm + 4 cm = 34 cm

Now, we can calculate the area of the rectangle formed by the frame:
Area of frame = Length of frame * Width of frame = 16 cm * 34 cm = 544 cm^2

Therefore, the area of the frame is 544 cm^2.