Question

what is the area of quadrilateral whose diagonal is 6.5 cm and altitude on the are diagonal are 4cm and 5cm

Answer 1

Answer is :

$(6.5 \times 5 \times \frac{1}{2} ) + (6.5 \times 4 \times \frac{1}{2} ) \\ = 16.25 + 13 \\ = 29.25$

Answer 2

Given: Length of diagonal is 6.5 cm And altitudes on the diagonal are 4 cm and 5 cm

To find: Area of quadrilateral

Step-by-step explanation:

As shown in figure

Area of quadrilateral ABCD = Area of triangle ADB + Area of triangle BCD

As we know area of triangle = $\dfrac{1}{2} \times base \times height$

So we have

In Δ ADB

$b_1=6.5 cm \text { and } h_1 = 4 cm$

In Δ BCD

$b_1=6.5 cm \text { and } h_1 = 5 cm$

$\text { area }= \dfrac{1}{2}\times +b_1 \times h_1 + \dfrac{1}{2}\times +b_2 \times h_2\\\\\Rightarrow area = \dfrac{1}{2}( 6.5 \times 4 + 6.5 \times 5)= \dfrac{1}{2} \times 6.5 (4+5)= 29.25 cm^2$

Hence the required area of quadrilateral is 29.25 cm ²