There is an octagonal shaped park as shown in the given figure. For finding its area, Priya and Divya divided it into two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?

Given that length of the sides of octagon = 5 m . Priya made two horizontal lines and divided the octagon into two trapeziums, whose parallel sides are 11 m and 5 m , respectively and the distance between the parallel sides is 4 m , and one rectangle having length and breadth 11 m and 5 m . Area of the trapezium = 1 2 × h × ( a + b ) = 1 2 × 4 × ( 11 + 5 ) = 2 × 16 = 32 m 2 . So, area of two trapezium = 2 × 32 = 64 m 2 . Area of Rectangle = Length × Breadth = 11 × 5 = 55 m 2 . Hence, the total area of octagon in Priya's method of division = 64 + 55 = 119 m 2 . Given that the length of the sides of octagon = 5 m . Divya divided the octagon vertically into two trapeziums whose parallel sides are 13 m and 5 m , respectively and distance between the parallel sides is 3 m and one rectangle having length and breadth 13 m and 5 m , respectively. Area of one trapezium = 1 2 × h × ( a + b ) = 1 2 × 3 × ( 13 + 5 ) = 1 2 × 3 × 18 = 3 × 9 = 27 m 2 . Area of two trapeziums = 2 × 27 = 54 m 2 . Area of Rectangle = Length × Breadth = 13 × 5 = 65 m 2 . Hence, the total area of octagon in Divya's method of division = 54 + 65 = 119 m 2 . Therefore, we observe that both Priya's and Divya's method of dividing the octagon and calculating the area of the octagon produce the same result which is 119 m 2 . Yes, one other way to calculate the area of the octagon is as per the following figure: Here, we extend the sides of the octagon to obtain a rectangle A B C D , whose lengths of opposite sides are A B = D C = 13 m and B C = A D = 11 m . Area of rectangle is = A B × B C = 13 × 11 = 143 m 2 . From this area, we shall subtract areas of four right angle triangles equal to A E F , considering its base as A E = 4 m and height as A F = 3 m . So, the total area of four such triangles equal to △ A E F = 4 × 1 2 × base × height = 4 × 1 2 × 4 × 3 = 2 × 4 × 3 = 24 m 2 . Hence, the area of the octagon is = 143 - 24 = 119 m 2 . Hence, we see that the value of the area obtained is the same as Priya and Divya obtained. Also, note that the area of the given octagon may be calculated by other methods as well.

E M B I B E

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2

Subject Experts Solutions for Chapter: Mensuration, Exercise 2: Worksheet 2

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Subject Experts Mathematics Solutions for Exercise - Subject Experts Solutions for Chapter: Mensuration, Exercise 2: Worksheet 2

Attempt the practice questions on Chapter 11: Mensuration, Exercise 2: Worksheet 2 with hints and solutions to strengthen your understanding. NCERT Practice Workbook Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from Subject Experts Solutions for Chapter: Mensuration, Exercise 2: Worksheet 2 with Hints & Solutions

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8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 2

A general quadrilateral can be split into two triangles by drawing one of its diagonal.

MEDIUM

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 2

Area of rhombus $= \frac{1}{2} \times$ product of diagonals.

MEDIUM

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 2

The area of trapezium becomes $4$ times, if its height gets doubled

HARD

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 2

The process of splitting a quadrilateral into two triangles is called triangulation.

HARD

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 2

A parallelogram can be divided into two congruent triangles by drawing a diagonal across it.

HARD

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 3

A polygon $A B C D E$ is divided into five parts as given below, where $AD = 10 cm, AH = 8 cm, AG = 5 \underline{cm}, AF = 2 cm, CH = 2 cm, BF = 3 cm$ and $EG = 3.5 cm .$

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If the area of polygon $A B C D E$ is $k {cm}^{2}$ , then find the value of $k$ .

MEDIUM

8th CBSE

IMPORTANT

NCERT Practice Workbook Mathematics>Chapter 11 - Mensuration>Worksheet 2>Q 3

Top surface of a raised platform is in the shape of a regular hexagon as shown in the given figure. If the area of the hexagonal surface is $k {cm}^{2}$ , then find $k$ up to two decimal places. [Use, $\sqrt{3} = 1.732$ ]

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