When we learn about shapes in math, two that often come up are squares and rectangles. Knowing how to figure out their areas is really important in Year 7 math.
Let’s see how to find the area of both shapes.
Area of a Square:
To find a square's area, use this formula:
[ \text{Area} = \text{side} \times \text{side} = \text{side}^2 ]
For instance, if one side of the square is 4 cm:
[ \text{Area} = 4 , \text{cm} \times 4 , \text{cm} = 16 , \text{cm}^2 ]
Area of a Rectangle:
To find a rectangle's area, use this formula:
[ \text{Area} = \text{length} \times \text{width} ]
Let’s say the length is 5 cm and the width is 3 cm:
[ \text{Area} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 ]
Now, let’s look at a square and a rectangle that have the same perimeter.
For example, if both a square and a rectangle have a perimeter of 16 cm:
For the square, each side is:
[ \text{side} = \frac{16 , \text{cm}}{4} = 4 , \text{cm} ]
So, the area is:
[ \text{Area}_\text{square} = 4 , \text{cm} \times 4 , \text{cm} = 16 , \text{cm}^2 ]
For the rectangle, if we pick a length of 5 cm and a width of 3 cm:
[ \text{Perimeter} = 2(\text{length} + \text{width}) = 2(5 + 3) = 16 , \text{cm} ]
The area is:
[ \text{Area}_\text{rectangle} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 ]
From these examples, we can see that squares and rectangles are both important shapes. However, their areas can be quite different based on their sizes. When you’re measuring, always remember to use the right formula for the shape you have!
When we learn about shapes in math, two that often come up are squares and rectangles. Knowing how to figure out their areas is really important in Year 7 math.
Let’s see how to find the area of both shapes.
Area of a Square:
To find a square's area, use this formula:
[ \text{Area} = \text{side} \times \text{side} = \text{side}^2 ]
For instance, if one side of the square is 4 cm:
[ \text{Area} = 4 , \text{cm} \times 4 , \text{cm} = 16 , \text{cm}^2 ]
Area of a Rectangle:
To find a rectangle's area, use this formula:
[ \text{Area} = \text{length} \times \text{width} ]
Let’s say the length is 5 cm and the width is 3 cm:
[ \text{Area} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 ]
Now, let’s look at a square and a rectangle that have the same perimeter.
For example, if both a square and a rectangle have a perimeter of 16 cm:
For the square, each side is:
[ \text{side} = \frac{16 , \text{cm}}{4} = 4 , \text{cm} ]
So, the area is:
[ \text{Area}_\text{square} = 4 , \text{cm} \times 4 , \text{cm} = 16 , \text{cm}^2 ]
For the rectangle, if we pick a length of 5 cm and a width of 3 cm:
[ \text{Perimeter} = 2(\text{length} + \text{width}) = 2(5 + 3) = 16 , \text{cm} ]
The area is:
[ \text{Area}_\text{rectangle} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 ]
From these examples, we can see that squares and rectangles are both important shapes. However, their areas can be quite different based on their sizes. When you’re measuring, always remember to use the right formula for the shape you have!