How To Find The Length and Width of a Rectangle Given The Perimeter
How To Find The Length and Width of a Rectangle Given The Perimeter

Question 08-Reigate Grammar 11 Plus Maths Entrance Examination 2021

The perimeter is the distance around the outside of a 2D shape. We can find the perimeter by adding the lengths of all the sides.

Example: The rectangle shown below has a length of 8 m and a width of 3 m.

Calculate the perimeter of the rectangle shown.

Solution: We know that the opposite sides of a rectangle are equal in length.

So, the two sides that are not labeled must also be 8 m and 3 m.

Perimeter = 8 + 8 + 3 + 3 = 22 m

The area of a 2D shape is the amount of space inside it. Commonly used units for the area are mm², cm², and m². We can find areas of 2D Shapes like squares, rectangles, triangles, etc. using a formula.

The table below shows the formulae for calculating the area for some of the most common 2D shapes:

In order to find the area, write down the formula of the 2D shape and substitute the values into the formula. Do the calculation and write the answer, including the units.

Example: Work out the area of the rectangle.

Solution: Area of rectangle = length x width

Let’s substitute the values of base and height into the formula.

Here the length is 8 cm and the width is 5 cm.

Area = 8 × 5 = 40

The measurements are in centimeters so the area will be measured in square centimeters.

Area = 40 cm²

Example: Find the area of the parallelogram.

Solution: Area of parallelogram = base × height

Let’s substitute the values of base and height into the formula.

Here the base is 8 mm and the height is 7 mm.

Area = 8 × 7 = 56

The measurements are in millimeters so the area will be measured in square millimeters.

Area = 56 mm²

Example: Work out the area of the triangle.

Solution: Area of triangle = 1⁄2 × base × height

Here the base is 10 m and the height is 8 m.

Area = 1⁄2 × 10 × 8 = 40 m²

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