Question

Calculate the area of a quadrilateral ABCD when length of a diagonal AC=10cm and the length of perpendiculars from B and D on AC be 5cm and 6cm respectively

Answer 1

Area of quadrilateral ABCD  is 55 $\mathrm{cm}^{2}$

Given:  

Length of diagonal = 10 cm,

Length of perpendicular from B = 5 cm,

From D = 6 cm

To find:

Area of a quadrilateral

Solution:

Area of a quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC

Area of a quadrilateral ABCD $=\left(\frac{1}{2} \times A C \times 5\right)+\left(\frac{1}{2} \times A C \times 6\right)$

$\begin{array}{l}{=\left(\frac{1}{2} \times 10 \times 5\right)+\left(\frac{1}{2} \times 10 \times 6\right)}\\ \\ {=\left(\frac{50}{2}\right)+\left(\frac{60}{2}\right)} \\ \\{=25+30}\end{array}$  

Area of quadrilateral ABCD  = 55 $\mathrm{cm}^{2}$

Answer 2

Answer:

Area of quadrilateral ABCD  is 55

Given:  

Length of diagonal = 10 cm,

Length of perpendicular from B = 5 cm,

From D = 6 cm

To find:

Area of a quadrilateral

Solution:

Area of a quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC

Area of a quadrilateral ABCD

 

Area of quadrilateral ABCD  = 55