Area of a Rectangle - Examples, Exercises and Solutions

Understanding Area of a Rectangle

Complete explanation with examples

How do we calculate the area of complex shapes?

When students hear the words "compound shapes", they usually feel uncomfortable. Just before you also ask yourself: "Oh, why this again?", you should be aware that there is no real reason. Describing shapes as compound doesn't really make them so. As it turns out calculating areas and perimeters of compound shapes is in fact relatively straightforward.

You will be introduced to Complex shapes only after you learn various shapes in geometry. The reason these shapes are complex is due to the fact that they are slightly different from those you've come to know. In each complex shape, additional shapes that you need to identify are hidden. Dividing the complex shape into several different (and familiar) shapes will allow you to answer the question of how to calculate the area of complex shapes.

The trick: extract a familiar shape from within the complex shape

So how do we answer the question of how to calculate the area of complex shapes? First, you need to identify familiar shapes within the complex shape. An example of this: a rectangle. As you know, each shape has properties that you are familiar with, so within the complex shape itself, you can apply the properties of the familiar shape and thus calculate areas and perimeters.

After completing the missing data (according to the properties of each shape, for example: rectangle), you can complete the "puzzle", identify additional data that is revealed to you, and thus calculate the area of the complex shape. When calculating the area of complex shapes, you will often need to perform simple arithmetic operations such as division and addition (mainly for sides in the shape) - all based on the unique properties of each shape.

Two composite shapes labeled with side lengths. • Left shape: A 'house-like' figure formed by a rectangle (4 units wide and 4 units high) with a triangle on top (two equal sides of 6 units, base 4 units). • Right shape: An L-shaped polygon composed of rec

Detailed explanation

Practice Area of a Rectangle

Test your knowledge with 122 quizzes

Look at the deltoid in the figure:

777444

What is its area?

Examples with solutions for Area of a Rectangle

Step-by-step solutions included
Exercise #1

Calculate the area of the right triangle below:

101010666888AAACCCBBB

Step-by-Step Solution

Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,

it can be argued that AB is the height of the triangle.

Hence we can calculate the area as follows:

AB×BC2=8×62=482=24 \frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24

Answer:

24 cm²

Video Solution
Exercise #2

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer:

96 cm²

Video Solution
Exercise #3

Calculate the area of the triangle ABC using the data in the figure.

121212888999AAABBBCCCDDD

Step-by-Step Solution

First, let's remember the formula for the area of a triangle:

(the side * the height that descends to the side) /2

 

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

CB×AD2 \frac{CB\times AD}{2}

8×92=722=36 \frac{8\times9}{2}=\frac{72}{2}=36

Answer:

36 cm²

Video Solution
Exercise #4

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer:

1912 19\frac{1}{2}

Video Solution
Exercise #5

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

Answer:

40 cm²

Video Solution

More Area of a Rectangle Questions

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Practice by Question Type

Applying the formula Calculate The Missing Side based on the formula Calculation using percentages Finding Area based off Perimeter and Vice Versa Identifying and defining elements Subtraction or addition to a larger shape Using additional geometric shapes Using external height Using Pythagoras' theorem Using ratios for calculation Using variables Verifying whether or not the formula is applicable Applying the formula Calculate The Missing Side based on the formula Calculating in two ways Finding Area based off Perimeter and Vice Versa Using additional geometric shapes Using congruence and similarity Using external height Using Pythagoras' theorem Using ratios for calculation Using variables Verifying whether or not the formula is applicable Applying the formula A shape consisting of several shapes (requiring the same formula) Calculate The Missing Side based on the formula Calculation using the diagonal Extended distributive law Finding Area based off Perimeter and Vice Versa Subtraction or addition to a larger shape Using additional geometric shapes Using Pythagoras' theorem Using ratios for calculation Using short multiplication formulas Using variables Worded problems Applying the formula Calculate The Missing Side based on the formula Finding Area based off Perimeter and Vice Versa Subtraction or addition to a larger shape Suggesting options for terms when the formula result is known Using additional geometric shapes Using Pythagoras' theorem Using ratios for calculation Using variables Applying the formula Ascertaining whether or not there are errors in the data Calculate The Missing Side based on the formula Calculating in two ways Extended distributive law Finding Area based off Perimeter and Vice Versa How many times does the shape fit inside of another shape? Identifying and defining elements Subtraction or addition to a larger shape Using additional geometric shapes Using congruence and similarity Using Pythagoras' theorem Using ratios for calculation Using variables Worded problems