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.
Area of Rectangle & Complex Shapes Practice Problems
Master rectangle area calculations and decompose complex shapes into familiar rectangles. Practice with step-by-step examples and build confidence solving geometry problems.
📚Practice Calculating Areas of Rectangles and Complex Shapes
- Calculate rectangle area using length × width formula
- Decompose complex shapes into familiar rectangles
- Apply rectangle properties to find missing dimensions
- Add and subtract rectangle areas in composite shapes
- Solve real-world rectangle area word problems
- Master the puzzle method for complex shape areas
Understanding Area of a Rectangle
Complete explanation with examples
How do we calculate the area of complex shapes?
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.
Practice Area of a Rectangle
Test your knowledge with 122 quizzes
Given the following rectangle:
Find the area of the rectangle.
Examples with solutions for Area of a Rectangle
Step-by-step solutions included
Exercise #1
Calculate the area of the parallelogram according to the data in the diagram.
Step-by-Step Solution
We know that ABCD is a parallelogram. According to the properties of parallelograms, each pair of opposite sides are equal and parallel.
Therefore:
We will calculate the area of the parallelogram using the formula of side multiplied by the height drawn from that side, so the area of the parallelogram is equal to:
Answer:
70
Video Solution
Exercise #2
Calculate the area of the right triangle below:
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:
Answer:
24 cm²
Video Solution
Exercise #3
ABDC is a deltoid.
AB = BD
DC = CA
AD = 12 cm
CB = 16 cm
Calculate the area of the deltoid.
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 #4
Calculate the area of the triangle ABC using the data in the figure.
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:
Answer:
36 cm²
Video Solution
Exercise #5
The trapezoid ABCD is shown below.
AB = 2.5 cm
DC = 4 cm
Height (h) = 6 cm
Calculate the area of the trapezoid.
Step-by-Step Solution
First, let's remind ourselves of the formula for the area of a trapezoid:
We substitute the given values into the formula:
(2.5+4)*6 =
6.5*6=
39/2 =
19.5
Answer:
Video Solution
Frequently Asked Questions
How do you find the area of a rectangle?
+The area of a rectangle is calculated using the formula: Area = length × width. Simply multiply the length by the width to get the total area in square units.
What is the easiest way to find the area of complex shapes?
+Break down complex shapes into familiar shapes like rectangles. Identify the rectangles within the complex shape, calculate each rectangle's area separately, then add or subtract these areas as needed.
How do you calculate missing dimensions in rectangle problems?
+Use the properties of rectangles: opposite sides are equal. If you know some dimensions, use addition and subtraction to find missing measurements based on the overall shape dimensions.
What are composite shapes in geometry?
+Composite shapes (also called compound shapes) are figures made up of two or more basic shapes combined together. They can be solved by breaking them into rectangles, triangles, or other familiar shapes.
Why do students struggle with complex shape area problems?
+Students often feel overwhelmed because complex shapes look complicated. The key is recognizing that these are just combinations of simple shapes you already know how to solve.
What math operations are needed for rectangle area problems?
+You'll primarily use: 1) Multiplication (length × width), 2) Addition (combining areas), 3) Subtraction (removing overlapping areas), 4) Basic arithmetic to find missing dimensions.
How do you solve L-shaped area problems?
+Divide the L-shape into two rectangles. Calculate each rectangle's area using length × width, then add the two areas together for the total area of the L-shaped figure.
What are common mistakes when calculating rectangle areas?
+Common errors include: mixing up length and width, forgetting to include units, adding dimensions instead of multiplying them, and not properly identifying rectangles within complex shapes.