Area of quadrilaterals

Area of parallelogram

The following quadrilaterals can be split into rectangles and triangles in order to calculate their area.

Diagram of a parallelogram and its base and height values

Method 1

Area\,of\,triangle\,1 = \frac{1}{2}bh

= \frac{1}{2} \times 4 \times 5

= \frac{1}{2} \times 20

= 10c{m^2}

Area of rectangle (2) = l \times b

= 6 \times 5

= 30c{m^2}

Area of triangle (3) = same as area of triangle (1)

= 10c{m^2}

Total\,area = 10 + 30 + 10 = 50c{m^2}

Method 2

A parallelogram split into two congruent triangles along the diagonal. Parallelogram is 5cm high and 10 cm long.

Split the parallelogram into two congruent triangles along one of the diagonals.

Area of triangle = \frac {1}{2}bh

= \frac {1}{2} \times 10 \times 5

= 25cm^{2}

Area of parallelogram = 2 \times 25 = 50 cm^{2}

Method 3

A parallelogram split into two congruent triangles along the diagonal. Parallelogram is 5cm high and 10 cm long.

Split the parallelogram into two congruent triangles along one of the diagonals.

Area\,of\,triangle\ = \frac{1}{2}bh

= \frac{1}{2} \times 10 \times 5

= 25{cm^2}

Area\ of\ parallelogram\ = 2 \times 25 = 50 {cm^2}

Area of a kite

Since a kite has a vertical line of symmetry, then triangles 1 and 2 will have the same area. This will also be the same for triangles 3 and 4.

Diagram of a 12cm x 28cm kite split into four right-angled triangles

Area\,of\,triangle\,1 = \frac{1}{2}bh

= \frac{1}{2} \times 6 \times 10

= \frac{1}{2} \times 60

= 30c{m^2}

Area of triangle 2 = 30c{m^2}

Area\,of\,triangle\,3 = \frac{1}{2}bh

= \frac{1}{2} \times 6 \times 18

= \frac{1}{2} \times 108

= 54c{m^2}

Area of triangle 4 = 54c{m^2}

Total\,area = 30 + 30 + 54 + 54 = 168c{m^2}