The rectangle is a quadrilateral with equal sides in pairs and with four right angles. To find the area of a rectangle, all you have to do is multiply the base by the height. To understand how to calculate the area of a rectangle, follow these simple steps.
Steps
Method 1 of 3: Understanding the Basic Characteristics of the Rectangle
Step 1. Understand what a rectangle is
The rectangle is a quadrilateral, which is a polygon formed by four sides. The opposite sides are the same, so the two bases and the two heights are the same. For example, if the side of a rectangle measures 10, the opposite side will also measure 10.
Furthermore, every square is also a rectangle, but not all rectangles are also squares. You can then calculate the area of a square by considering it a rectangle
Step 2. Memorize the formula for calculating the area of a rectangle
The formula is simple: A = b * h. It means that the area is equal to the base multiplied by the height.
Method 2 of 3: Find the Area of a Rectangle
Step 1. Find out the size of the base
In most problems this will be given to you, otherwise you can find it with a ruler.
Note that the double sign on the bases of the rectangle in the figure indicates that they are equal to each other
Step 2. Find the height of the rectangle
Use the method above.
Note that the mark on the two heights of the rectangle in the figure indicates that they are equal to each other
Step 3. Write the base and height measurements side by side
In our example, the base is 5 cm and the height 4 cm.
Step 4. Multiply the base by the height
The base is 5 cm and the height is 4 cm, so to find the area just substitute these values in the formula A = b * h.
- A = 4cm * 5cm
- A = 20 cm ^ 2
Step 5. Express the result in square centimeters
The final result is 20 cm ^ 2, or "twenty square centimeters".
You can write the final result in two ways: either 20 cmq or 20 cm ^ 2
Method 3 of 3: Find the Area Knowing only one of the two Dimensions and the Diagonal
Step 1. Understand the Pythagorean theorem
The Pythagorean theorem is a formula to find the third side of a right triangle knowing the measure of the other two. You can use it to find the hypotenuse of a triangle, which is the longest side, or one of the two legs, which are the sides that form the right angle.
- Since the rectangle is made up of four right angles, the diagonal that divides the figure in half will form two right triangles, to which you can apply the Pythagorean theorem.
- The theorem is: a ^ 2 + b ^ 2 = c ^ 2, where a and b are the legs and c is the hypotenuse.
Step 2. Use the Pythagorean theorem to find the missing dimension of the triangle
Let's say you have a rectangle with a base of 6 cm and a diagonal of 10 cm. Use 6 cm as the first catheter, b for the other and 10 cm as the hypotenuse. In short, it is enough to replace the known measures in the formula of the Pythagorean theorem and solve. That's how:
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Ex:
6 ^ 2 + b ^ 2 = 10 ^ 2
- 36 + b ^ 2 = 100
- b ^ 2 = 100 - 36
- b ^ 2 = 64
- Square root (b) = square root (64)
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b = 8
The measure of the other side of the rectangle, which corresponds to the other dimension of the rectangle, is 8 cm
Step 3. Multiply the base by the height
Now that you have used the Pythagorean theorem to find the base and height of the rectangle, you just need to multiply them together.
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Ex:
6cm * 8cm = 48cm ^ 2
Step 4. Express the result in square centimeters
The final result is 48 cm ^ 2, or 48 cm2.
Advice
- All squares are rectangles, but not all rectangles are squares.
- When you have to calculate the area of a polygon, the result must always be expressed squared.
