picture is painted cardboard 50cm long 30cm wide there is a margin 2.5cm along each side .find the total area of margin, class 7 solve measurements
HINT: First find the area with margin, i.e., add the margin measurement to the length and breadth and find the area. Then find the area without the margin (area with the given measurements WITHOUT any additions). Subtract the second area from the first, and you should get your answer.
To find the total area of the margin, we need to subtract the area of the inner rectangle (the painted cardboard) from the area of the outer rectangle (the entire piece of cardboard).
Let's first find the area of the inner rectangle (the painted cardboard). The length of the painted cardboard is 50cm, and the width is 30cm. So, the area of the painted cardboard is:
Area of inner rectangle = Length × Width
= 50cm × 30cm
= 1500 square cm
Now, let's find the length and width of the outer rectangle by adding twice the margin to each side of the painted cardboard.
Length of the outer rectangle = Length of inner rectangle + 2 × Margin
= 50cm + 2 × 2.5cm
= 50cm + 5cm
= 55cm
Similarly,
Width of the outer rectangle = Width of inner rectangle + 2 × Margin
= 30cm + 2 × 2.5cm
= 30cm + 5cm
= 35cm
Now, find the area of the outer rectangle:
Area of outer rectangle = Length × Width
= 55cm × 35cm
= 1925 square cm
Finally, we can find the area of the margin by subtracting the area of the inner rectangle from the area of the outer rectangle:
Area of margin = Area of outer rectangle - Area of inner rectangle
= 1925 square cm - 1500 square cm
= 425 square cm
Therefore, the total area of the margin is 425 square cm.