Area of quadrilaterals

Area of quadrilaterals

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2. PRESENTED BY Mathematics Optional 2

3. INTRODUCTION Quadrilateral Family parallelogram rectangle rhombus square trapezium A quadrilateral is a four-sided plane. 3

4. PRESENTATION Area of a Parallelogram The area of a parallelogram is the product of the length of one side and the distance to the opposite side. a = b * h 4

5. Area of a Rhombus The area of a rhombus is half the product of the diagonals. 5

6. Area of a Trapezium The area of a trapezium is half the product of the sum of its parallel sides and the distance between them. a = * h * ( b 1 + b 2 ) 6

7. Area of a Quadrilateral The area of a quadrilateral is half the product of the length of a diagonal with the sum of the lengths of the perpendiculars from the opposite vertexes. a = * d * ( p 1 + p 2 ) 7

8. Area Relations The area of the trapezium shown below is 8

9. If a and b are equal in the trapezium it becomes a parallelogram. When the angles of this parallelogram are made right angles it becomes a rectangle. 9

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12. REVIEW Formula In general Type of Quadrilateral Area Formula Rectangle A = b*h Square A = s ² Parallelogram A = b*h Rhombus A = (1/2)(d1 * d2) Trapezium A = (1/2)h(b1 + b2) Quadrilateral A = (1/2)d(p1 + p2) Key: b – base h – height s - side d - diagonal b1/b2 – base1/base2 d1/d2 – diagonal1/diagonal2 p1/p2 – perpendicular1/ perpendicular1 12

13. 1 . Find the area of the parallelogram of height 5cm and base 12cm. A = b * h = 5 * 12 = 60 cm ² FOLLOW UP ACTIVITY Examples 13

14. 2. Find the area of the rhombus whose diagonals are of length 16cm and 12cm. A = (1/2)(d1 * d2) = (1/2)(16 * 12) = 96 cm ² 14

15. 3. Find the area of the trapezium of height 4cm and parallel sides 6cm and 9cm. A = (1/2)h(b1 + b2) = (1/2)(4)(9 + 6) = (1/2)(60) = 30 cm ² 9cm 6cm 4cm 15

16. 4. Find the area of a quadrilateral having diagonal 50cm and perpendicular heights measuring 10cm and 20cm. A = (1/2)d(p1 + p2) = (1/2)(50)(10+20) = (1/2)(1500) = 750 cm ² 16

17. Assignment 1. Find the area of the Trapezium below 2. The diagonals of a quadrilateral are perpendicular to each other and their lengths are 16cms and 10cms. What is its area? 17