Question

F
3 Find the area of a quadrilateral ABCD
in which diagonal BD = 14 cm, and
perpendiculars from vertices A and C
measure 10 cm and 14 cm respectively.
A​

Answer 1

Answer:

Step-by-step explanation:

Let the quadrilateral be divided into 2 triangles: ΔABD and ΔBDC

In ΔABD,

we know that perpendicular from a to DB = 10 cm

Let this perpendicular be AX.

Area of a triangle = 1/2 * base * height

B=14

H=10

subst. values,   1/2 * 14 *10 = 70cm² --------(1)

similarly, in ΔBDC,

B=14cm

H=14cm

Area of triangle = 1/2 * 14 * 14 = 98cm² --------(2)

Total area of quadrilateral = sum of the areas of the triangles

⇒ we have to add (1) and (2)

⇒ 70cm² + 98cm²

= 168 cm²

Hence, the area of the quadrilateral = 168 cm²

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