A picture frame is 20 cm by 30 cm. This includes a border (the shaded region) 5 cm wide surrounding the picture itself. What is the area of this shaded border in sq cm?
just subtract the picture area from the total:
(20)(30)-(20-10)(30-10)
To find the area of the shaded border, we need to subtract the area of the picture from the total area of the frame.
The total area of the frame is given by the length multiplied by the width, which is 20 cm multiplied by 30 cm:
Total area of the frame = 20 cm * 30 cm = 600 sq cm
To find the area of the picture, we need to subtract the width of the border from the total width and the length of the border from the total length. The width of the picture is the total width minus twice the width of the border:
Width of the picture = Total width - 2 * Width of the border
Width of the picture = 20 cm - 2 * 5 cm = 20 cm - 10 cm = 10 cm
Similarly, the length of the picture is the total length minus twice the width of the border:
Length of the picture = Total length - 2 * Width of the border
Length of the picture = 30 cm - 2 * 5 cm = 30 cm - 10 cm = 20 cm
The area of the picture is then the width multiplied by the length:
Area of the picture = Width of the picture * Length of the picture
Area of the picture = 10 cm * 20 cm = 200 sq cm
Finally, we can find the area of the shaded border by subtracting the area of the picture from the total area:
Area of the shaded border = Total area of the frame - Area of the picture
Area of the shaded border = 600 sq cm - 200 sq cm = 400 sq cm
Therefore, the area of the shaded border is 400 square centimeters.
To find the area of the shaded border surrounding the picture, we first need to calculate the area of the entire picture frame and then subtract the area of the actual picture.
The picture frame is given as 20 cm by 30 cm, which means its dimensions are 20 cm in width and 30 cm in height. We are also told that there is a border around the picture itself, which is 5 cm wide on all sides.
To calculate the area of the picture frame, we can use the formula:
Area = length × width
In this case, the length of the frame is 30 cm (including the picture and the border), and the width is 20 cm (including the picture and the border). So, the area of the entire picture frame is:
Area of frame = 30 cm × 20 cm = 600 sq cm.
Now, we need to subtract the area of the actual picture from the total area of the frame in order to find the area of the shaded border.
Since the width of the border is 5 cm on each side, the picture dimensions must be reduced by 10 cm in both width and height. Therefore, the picture dimensions are 10 cm less in each dimension, resulting in a width of 20 cm - 10 cm = 10 cm and a height of 30 cm - 10 cm = 20 cm.
To find the area of the picture, we use the same formula as before:
Area = length × width
So, the area of the picture is:
Area of picture = 10 cm × 20 cm = 200 sq cm.
Finally, to find the area of the shaded border, we subtract the area of the picture from the area of the entire frame:
Area of shaded border = Area of frame - Area of picture
= 600 sq cm - 200 sq cm
= 400 sq cm.
Therefore, the area of the shaded border is 400 square centimeters.