Question

In a quadrilateral abcd , ac=15cm. The perpendicular drawn from b and d respectively to ac measure 8.2 and 9.1 find the area of quadrilateral

Answer 1

We know,
Ar. of a quadrilateral
$= \frac{1}{2} \times diagonal1 \times (length \: of \: the \: perpendiculars \: from \: the \: remaining \: two \: angles$
$= \frac{1}{2} \times 15 \times (8.2 + 9.1)$
=7.5×17.3
=129.75

Answer 2

Given:

In a quadrilateral ABCD, AC = 15cm

To Find:

the area of the quadrilateral.

Solution:

The area of a quadrilateral will be equal to the area of the two triangle

So, area of ΔADC + area of ΔABC = area of the quadrilateral

The formula to calculate the area of a triangle is 1/2 × base × height

So, the area of ΔADC = 1/2× AC× DE

Now, we substitute the values

ΔADC = 1/2 × 15  × 9.1

ΔADC = 68.25cm²

Now, the area of ΔABC

ΔABC = 1/2× AC× BF

ΔABC = 1/2 × 15 × 8.2

ΔABC = 61.5cm²

Now the area of the quadrilateral ABCD = area of triangle ADC + area of triangle ABC

                                                                   = 68.25 + 61.5

                                                                   = 129.75cm²

Therefore the area of the quadrilateral ABCD = 129.75cm².