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Chapter 9: Area of Plane Figures

    Introduction

    Area of a Trapezium

    Area of a Quadrilateral

    Area of a Rhombus

    Surveying the Field

    Area of a Polygon

    Area of a Circle

    Area of a Circular Path or Area of a Ring

    Length of the Arc

    Area of Sector

    Exercise 9.1

    Exercise 9.2

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 9: Area of Plane Figures > Area of a Quadrilateral

Area of a Quadrilateral

Any quadrilateral can be divided into two by drawing a diagonal. This principle helps us calculate the total area.

Consider quadrilateral PQRS:

  • Draw diagonal PR to split it into two triangles

  • From points Q and S, draw perpendicular lines to PR

  • Let's call these heights h₁ and h₂ respectively

  • Let's call the diagonal length 'L'

Thus, we have:

Area of triangle PQR = × ×

Area of triangle RSP = × ×

Total area of PQRS = 12 × L × (h₁ + h₂)

This can be written as:

Area = 12 × d × (h₁ + h₂) , where 'd' is the diagonal length

Instructions

A field has the shape of a quadrilateral WXYZ. A surveyor measures the diagonal WY as 100 meters. The perpendicular distances from points X and Z to this diagonal are 45 meters and 35 meters respectively. Find the area of the field.
We know: d = m, h₁ = m and h₂ = 35 m
Area = × × (45 + 35) = × × = square meters

Instructions

An architect is designing a uniquely shaped courtyard DEFG. The diagonal EG is 24 meters, and the perpendicular heights from D and F to this diagonal are 8 meters and 12 meters respectively. (a) What is the area of the courtyard? (b) If the cost of flooring is Rs. 50 per square meter, what will be the total cost of flooring the courtyard?
(a) Area calculation: d = m, h₁ = 8m and h₂ = m
Area = × × (8 + 12) Area = × × = square meters
(b) Cost calculation: Cost per square meter = Rs.
Total cost = × Rs. 50 = Rs.