Area of Combined Figures

A combined figure is a geometrical shape that is the combination of many simple geometrical shapes. 


To find the area of combined figures we will follow the steps:

Step I: First we divide the combined figure into its simple geometrical shapes. 

Step II: Then calculate the area of these simple geometrical shapes separately, 

Step III: Finally, to find the required area of the combined figure we need to add or subtract these areas.

Solved Examples on Area of combined figures:

1. Find the area of the shaded region of the adjoining figure. (Use π = \(\frac{22}{7}\))

Area of Combined Figures

JKLM is a square of side 7 cm. O is the centre of the semicircle MNL.

Solution:

Step I: First we divide the combined figure into its simple geometrical shapes.

The given combined shape is combination of a square and a semicircle.

Step II: Then calculate the area of these simple geometrical shapes separately.

Area of the square JKLM = 72 cm2

                                    = 49 cm2

Area of the semicircle LNM = \(\frac{1}{2}\) π ∙ \((\frac{7}{2})^{2}\) cm2 , [Since, diameter LM = 7 cm]

                                       = \(\frac{1}{2}\)  ∙  \(\frac{22}{7}\) ∙ \(\frac{49}{4}\) cm2

                                       = \(\frac{77}{4}\) cm2

                                       = 19.25 cm2

Step III: Finally, add these areas up to get the total area of the combined figure.

Therefore, the required area = 49 cm2 + 19.25 cm2

                                          = 68.25 cm2.


2. In the adjoining figure, PQRS is a square of side 14 cm and O is the centre of the circle touching all sides of the square. 

Area of a Composite Figure

Find the area of the shaded region.

Solution:

Step I: First we divide the combined figure into its simple geometrical shapes.

The given combined shape is combination of a square and a circle.

Step II: Then calculate the area of these simple geometrical shapes separately.

Area of the square PQRS = 142 cm2

                                    = 196 cm2

Area of the circle with centre O = π ∙ 72 cm2, [Since, diameter SR = 14 cm]

                                             = \(\frac{22}{7}\) ∙ 49 cm2

                                             = 22 × 7 cm2

                                             = 154 cm2

Step III: Finally, to find the required area of the combined figure we need to subtract the area of the circle from the area of the square.

 

Therefore, the required area = 196 cm2 - 154 cm2

                                          = 42 cm2


3. In the adjoining figure alongside, there are four equal quadrants of circles each of radius 3.5 cm, their centres being P, Q, R and S. 

Area of Compound Shapes

Find the area of the shaded region.

Solution:

Step I: First we divide the combined figure into its simple geometrical shapes.

The given combined shape is combination of a square and four quadrants.

Step II:Then calculate the area of these simple geometrical shapes separately.

Area of the square PQRS = 72 cm2, [Since, side of the square = 7 cm]

                                                = 49 cm2

Area of the quadrant APB = \(\frac{1}{4}\) π ∙ r2 cm2

                                = \(\frac{1}{4}\) ∙ \(\frac{22}{7}\)  ∙  \((\frac{7}{2})^{2}\) cm2, [Since, side of the square = 7 cm and radius of the quadrant = \(\frac{7}{2}\) cm]

                                = \(\frac{77}{8}\) cm2

There are four quadrants and they have the same area.

So, total area of the four quadrants = 4 × \(\frac{77}{8}\) cm2

                                                    = \(\frac{77}{2}\) cm2

                                                    = \(\frac{77}{2}\) cm2

Step III: Finally, to find the required area of the combined figure we need to subtract the area of the four quadrants from the area of the square.

Therefore, the required area = 49 cm2 - \(\frac{77}{2}\) cm2

                                          = \(\frac{21}{2}\) cm2

                                          = 10.5 cm2




10th Grade Math

From Areas of Combined Figures to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 22, 24 04:21 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  2. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  3. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More

  4. Place Value | Place, Place Value and Face Value | Grouping the Digits

    Feb 19, 24 11:57 PM

    Place-value of a Digit
    The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details. We know th…

    Read More

  5. Math Questions Answers | Solved Math Questions and Answers | Free Math

    Feb 19, 24 11:14 PM

    Math Questions Answers
    In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students

    Read More