In the given figure, ABCD is a quadrilateral-shaped field in which dia

1.	In the given figure, ABCD is a quadrilateral-shaped field in which diagonal BD is 36 m, AL ⊥ BD and CM ⊥ BD such that AL = 19m and CM = 11m. Find the area of the field.
Answer» Given: A quadrilateral ABCD \(AL\perp BD\) and \(CM\perp BD\) AL = 19 cm BD = 36 cm CM = 11 cm Here, Area (quad. ABCD) = area (△ABD) + area (△ACD) Area of triangle = \(\frac{1}{2}\)× (base) × (height). Therefore Area of quad ABCD = \(\frac{1}{2}\)× (BD) × (AL) + \(\frac{1}{2}\)× (BD) × (CM) = \(\frac{1}{2}\)× (36) × (19) + \(\frac{1}{2}\)× (36) × (11) = 342 + 198 = 540 cm² Therefore area of the quadrilateral ABCD is 540 cm².

In the given figure, ABCD is a quadrilateral-shaped field in which diagonal BD is 36 m, AL ⊥ BD and CM ⊥ BD such that AL = 19m and CM = 11m. Find the area of the field.

Answer»

Given: A quadrilateral ABCD

\(AL\perp BD\) and \(CM\perp BD\)

AL = 19 cm

BD = 36 cm

CM = 11 cm

Here,

Area (quad. ABCD) = area (△ABD) + area (△ACD)

Area of triangle = \(\frac{1}{2}\)× (base) × (height).

Therefore

Area of quad ABCD = \(\frac{1}{2}\)× (BD) × (AL) + \(\frac{1}{2}\)× (BD) × (CM)

= \(\frac{1}{2}\)× (36) × (19) + \(\frac{1}{2}\)× (36) × (11) = 342 + 198 = 540 cm²

Therefore area of the quadrilateral ABCD is 540 cm².