A quadrilateral with four right angles is known as a rectangle in maths. A parallelogram with a right angle can also be described this way: if one angle is right, the others must be as well. Furthermore, the length of each side of a rectangle is equal to the length of the opposite side. In contrast to a square, which is a special case of a rectangle, it also has unequal adjacent sides.
The name of a shape usually explains a lot if you know Latin. Rectangulus is a Latin word that means rectangle. It’s a combination of rectus (which means “right, straight”) and angulus (which means “angle”) so it could be used to define a rectangle simply.
Rectangles are a fun way to start learning basic geometry. They introduce you to algebra, geometry, area, and perimeter concepts in maths.
What are the properties of a rectangle?
Rectangles have a lot of interesting characteristics:
- A rectangle is cyclic, which means that all of its corners are connected by a single circle.
- It is equiangular, meaning that all of its corner angles are 90 degrees.
- Its sides meet at right angles, making it rectilinear.
- Through the center, there are two lines of reflectional symmetry: vertical and horizontal.
- There are two diagonals that cross each other. The Pythagorean theorem can be used to calculate the diagonal length.
- A rectangle’s opposite sides are parallel to each other and have the same length.
What is area?
The area of a shape is a measurement of how much space it contains. Calculating the area of a shape or surface is helpful in daily life when you need to know how much paint to buy to cover a wall or how much grass seed to sow a lawn, for example.
The area of a shape refers to the amount of two-dimensional space it occupies. It’s expressed in squares, such as square centimeters, square meters, and square kilometers.
What is length and width?
The term “length” refers to the size of an object or the distance between two points. The length of an object or the distance between two points is measured in length. It’s used to determine the size of an object or the distance between two points.
The longest side of an object is its extended dimension or length. Width, quite simply, denotes the measurement between two points. Unlike length, width refers to the shorter side of a rectangle.
Unit of Area
The amount of space inside a 2D shape is measured by its area. The unit of length will depend on the unit of area, however the following are common in maths questions:
- Square kilometers (km2)
- Square meters (m2)
- Square centimeters (cm2)
- Square millimeters (mm2)
What is the area of a rectangle?
Area is a two-dimensional concept with a length and width in maths. The area of a rectangle is obtained by multiplying its length by its width.
What is the formula to find the area of a rectangle?
Multiply the length by the width to get solutions for surface area of a rectangle. The formula is as follows:
A = L x W, where A denotes area, L denotes length and W denotes width.
What is the difference between the area and perimeter of a rectangle?
Unlike area, the perimeter of a rectangle is found by adding the lengths of its four sides. A rectangle’s perimeter is therefore obtained by using the formula P=2l+2w, where “l” is the rectangle’s length and “w” is its width.
Questions and solutions to find the area of a rectangle
Question 1
There are two main things to look out for:
- Unit of measurements: In this example, the unit of measurement is centimeters (cm) meaning the area of this rectangle will be in centimeters squared (cm2).
- Formula notation: You should know which side is the length, and which is the width. In this example, width is 13 cm as it’s always the shorter side. As such, the length is 28 cm.
To find the area:
Area = L x W
Area = 13 cm x 28 cm
Area = 364 cm2
Question 2
This question is slightly more complex than the previous one. Let’s follow the steps we did in the previous example:
- Unit of measurements: In this example, the unit of measurement is centimeters (cm) for the width, but the length is in meters (m). The question may specify which unit of measurement the answer should be in, but if not then choose the largest notation: (Millimeters < centimeters < meters < kilometers). Smaller numbers are easier to work with so we will work in meters!
- Formula notation: Since width is the short side, in this example it’s 200 cm. As such, the length is 18 m.
Now to find the solutions to the area:
If 200 cm = 2 m
Therefore, Area = 2 m x 18 m
Area = 36 m2
How do you find the area of an irregular rectangle?
You may need to locate the area of a shape that is not a regular shape on occasion. One way to find the area of an irregular shape is to divide it into smaller shapes for which you already have the formula. Then you sum up all the areas that form the shape.
Area of simple irregular rectangles
There are multiple ways to find the solutions to the area of an irregular rectangle – all of which use the same formula mentioned. Here’s an example of an irregular rectangle:
The first thing to do is to split the irregular rectangle as shown below and find the separate areas and add them together.
The second thing to do is extend the shape into a larger rectangle and then subtract the smaller rectangle from it.
Irregular Rectangle Example
The total area is the sum of the area of rectangle A and rectangle B.
Rectangle B’s area is:
Area = 17 cm x 4 cm
Area B = 68 cm2
The area of rectangle A is more complex, but don’t panic! You need to find length of the top side of rectangle A:
Top side length = 37 cm – 17 cm
Length = 20 cm
Area = 13 cm x 20 cm
Area A = 260 cm2
Now that you have both areas for rectangle A and B, you can add them to get the total area of the irregular rectangle:
Total area = 68 cm2 + 260 cm2
Total area = 328 cm2
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