Area of Quadrilaterals and Other Polygons - Mathematics Form 2 Notes

• Quadrilaterals.
  
  • Area of rectangle
  • Area of Parallelogram
  • Area of a Rhombus
  • Area of Trapezium
• Area of regular polygons
• Past KCSE Questions on the Topic.

Quadrilaterals.

• They are four sided figures e.g. rectangle, square, rhombus, parallelogram, trapezium and kite.

Area of Rectangle

A = L X W

AB and DC area the lengths while AD and BC are the width.

Area of Parallelogram

A figure whose opposite side are equal parallel.

Area = base x height = 2.5 x 1.8 = 4.5 cm²

Area of a Rhombus

A figure with all sides equal and the diagonals bisect each other at 900. In the figure below BC = CD = DA = AB = 4 cm while AC=10 cm and BD = 12. Find the area

Solution

Find half of the diagonal which is ¹/₂ ×10 = 5 cm
Area of ∆ BCD = ¹/₂ × 12 × 5 = 30 cm²
Area of ∆ABCD = 2 × area of ∆BCD
= 2 × 30cm²
= 60 cm²

Area of Trapezium

A quadrilateral with only two of its opposite sides being parallel. The area = ¹/₂(a+b)h

Example

Find the area of the above figure

Solution

Area = ¹/₂(6+12)4
= 9 x 4 = 36 cm²

Note:

You can use the sine rule to get the height given the hypotenuse and an angle.

sin θ = opposite
          hypoteneus
Or use the acronym SOHCAHTOA

Rhombus

Example

In the figure above the lines market // =7 cm while / =5 cm, find the area.

Solution

Join X to Y.
Find the area of the two triangles formed
¹/₂x 5 x 5x sin95⁰= 12.45 (Triangle one)
¹/₂x 7 x 7x sin60⁰= 21.21 (Triangle two)
Then add the area of the two triangles
12.45 + 21.21 = 33.67 cm²

Area of Regular Polygons

Any regular polygon can be divided into isosceles triangle by joining the vertices to the Centre.

The number of the polygon formed is equal to the number of sides of the polygon.

Example

If the radius is of a pentagon 6 cm find its area.

Solution

Divide the pentagone into five triangles each with 72^oi.e. (³⁶⁰/₅ )
Area of one triangle will be = ¹/₂ x 6 x 6 xsin 72^o
=17.11
There are five triangles therefore
Area = 5 × 17.11
= 85.55cm²

Past KCSE Questions on the Topic.

1. The diagram below, not drawn to scale, is a regular pentagon circumscribed in a circle of radius 10 cm at centre O
   
   Find
   1. The side of the pentagon (2mks)
   2. The area of the shaded region (3mks)
2. PQRS is a trapezium in which PQ is parallel to SR, PQ = 6cm, SR = 12cm, ∠PSR = 40⁰ and PS = 10 cm. Calculate the area of the trapezium. (4mks)
   
   
3. A regular octagon has an area of 101.8 cm². calculate the length of one side of the octagon (4marks)
4. Find the area of a regular polygon of length 10 cm and side n, given that the sum of interior angles of n : n – 1 is in the ratio 4 : 3.
5. Calculate the area of the quadrilateral ABCD shown:-