Question

What is area of quadrilateral ? Plz with examples

Answer 1

Answer:

${1}{2} \times \; diagonal \times (Sum \; of \; height \; of \; two \; triangle)$

Step-by-step explanation:

Area of Quadrilateral Formula⤵️

• Consider a quadrilateral PQRS, of different(unequal) lengths, let us derive a formula for the area of a quadrilateral.
• We can view the quadrilateral as a combination of 2 triangles, with the diagonal PR being the common base.
• h¹ and h² are the heights of triangles PSR and PQR respectively.
• Area of quadrilateral PQRS is equal to the sum of the area of triangle PSR and the area of triangle PQR.
• Area of triangle PSR = (base * height)/2 = (PR * h¹)/2
• Area of triangle PQR = (base * height)/2 = (PR* h²)/2
• Thus, area of quadrilateral PQRS is,
• Area of triangle PSR + Area of triangle PQR =

$= {PR \times h_{1}}{2} + \frac{PR \times h_{2}}{2} = PR \left ( \frac{h_{1}+ h_{2}}{2} \right )</p><p>$

$\frac{1}{2} PR \times (h_{1}+ h_{2})$

Hence, the area of a quadrilateral formula is,

✔️Area of a general Quadrilateral

${1}{2} \times \; diagonal \times (Sum \; of \; height \; of \; two \; triangle)$

Area of a Quadrilateral Example⤵️

✔️Question:

In the given quadrilateral ABCD, the side BD = 15 cm and the heights of the triangles ABD and BCD are 5 cm and 7 cm respectively. Find the area of the quadrilateral ABCD.

Area Of Quadrilateral Example

Solution:⤵️

Diagonal = BD = 15 cm

Heights, h1=5 cm & h2=7 cm

Sum of the heights of the triangles = h1 + h2 = 5 + 7 = 12 cm

Thus, area of quadrilateral ABCD =

$= {1}{2} \times \; diagonal \times (Sum \; of \; height \; of \; two \; triangle)$

= (15 * 12)/2 = 90 cm²