my exams are starting from next week i am facing so much problems in perimeter and area of simple geometrical figures . my question is ;find the area , in square centimetres , of a rectangular strip of board 3.28 m long and 75 mm wide . the second question is ; a square cardboard of side 1.2 m has a 10 cm wide border round the exterior of three of its sides . find the area of the border. if you don't mind can you solve the question which i asked so i can solve the rest of the question easily.

for any rectangle, the area is length * width.

So, get out your calculator and punch in your numbers.

watch out for the units. you can't mix m and cm.

For the cardboard with the border, the whole thing with border on 4 sides has area (120+10+10)^2 = 19600 cm^2
The inside cardboard has area 14400 cm^2
So, a full 4-sided border would have area 5200 cm^2. But, you only have a border on 3 sides, so you need to subtract 1/4 of that, leaving 3900 cm^2.
But that includes a little 10x10 corner, so lop off that 100 cm^2 leaving 3800 cm^2 of border.

425cm.sq

To find the area of a rectangular strip of board, you can use the formula:

Area = Length × Width

Given:
Length of the board = 3.28 m
Width of the board = 75 mm

First, we need to ensure that the lengths and widths are in the same unit. Since the width is given in millimeters, we need to convert it to meters.

1 meter = 1000 millimeters

So, the width in meters will be:

Width = 75 mm ÷ 1000 = 0.075 m

Now, we can substitute the values in the formula:

Area = 3.28 m × 0.075 m

Multiply the values:

Area = 0.246 m²

Therefore, the area of the rectangular strip of board is 0.246 square meters.

Now, moving on to the second question about the square cardboard:

To find the area of the border, we first need to calculate the area of the larger square, including the border, and then subtract the area of the original square.

Given:
Side of the square cardboard = 1.2 m
Width of the border = 10 cm

First, we convert the width of the border into meters:

Width = 10 cm ÷ 100 = 0.1 m

The length of the larger square will be the same as the original square, so we can calculate the area including the border:

Area of the larger square = (Side + 2 × Width) × Side

Area of the larger square = (1.2 m + 2 × 0.1 m) × 1.2 m

Area of the larger square = 1.4 m × 1.2 m

Multiply the values:

Area of the larger square = 1.68 m²

Next, we calculate the area of the original square:

Area of the original square = Side × Side

Area of the original square = 1.2 m × 1.2 m

Multiply the values:

Area of the original square = 1.44 m²

Finally, we can find the area of the border by subtracting the area of the original square from the area of the larger square:

Area of the border = Area of the larger square - Area of the original square

Area of the border = 1.68 m² - 1.44 m²

Subtract the values:

Area of the border = 0.24 m²

Therefore, the area of the border is 0.24 square meters.