A diagonal of a quadrilateral is 40 m long and the perpendiculars to i

1.	A diagonal of a quadrilateral is 40 m long and the perpendiculars to it from the opposite corners are 8 m and 10 m respectively. Find its area.
Answer» GIVEN :- A diagonal of a quadrilateral is 40 m long and the perpendiculars to it from the opposite corners are 8 m and 10 m respectively. Have to Find :- Find the area $.$ Solution :- As we know the formula of area of quadrilateral (½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices. ↬ ½ × d × ( sum of lengths ) Here , D = 40 m Lengths = 8 m and 10 m respectively. Therefore, Substituting the VALUES in the above formula , ↬ ½ × 40 × ( 8 + 10 ) ↬ ½ × 40 × 18 $\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{40}\times{\cancel{{18}}}}$ ↬ 40 × 9 ↬ 360 m² ____________________________ ★ Some Important Formulas ★ ➤ Perimeter of Rectangle = 2( L + B ) ➤ Perimeter of square = 4 × SIDE ➤ Perimeter of triangle = AB + BC + CA ➤ Area of Rectangle = L × B ➤ Area of Square = ( side ) ² ➤ Area of Rhombus = Product of Diagonal/2. ➤ Area of Parallelogram = Base × Height. ➤ Area of triangle = 1/2 × base × height .

A diagonal of a quadrilateral is 40 m long and the perpendiculars to it from the opposite corners are 8 m and 10 m respectively. Find its area.

Answer»

GIVEN :-

A diagonal of a quadrilateral is 40 m long and the perpendiculars to it from the opposite corners are 8 m and 10 m respectively.

Have to Find :-

Find the area $.$

Solution :-

As we know the formula of area of quadrilateral

(½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices.

↬ ½ × d × ( sum of lengths )

Here ,

D = 40 m

Lengths = 8 m and 10 m respectively.

Therefore,

Substituting the VALUES in the above formula ,

↬ ½ × 40 × ( 8 + 10 )

↬ ½ × 40 × 18

$\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{40}\times{\cancel{{18}}}}$

↬ 40 × 9

↬ 360 m²

____________________________

★ Some Important Formulas ★

➤ Perimeter of Rectangle = 2( L + B )

➤ Perimeter of square = 4 × SIDE

➤ Perimeter of triangle = AB + BC + CA

➤ Area of Rectangle = L × B

➤ Area of Square = ( side ) ²

➤ Area of Rhombus = Product of Diagonal/2.

➤ Area of Parallelogram = Base × Height.

➤ Area of triangle = 1/2 × base × height .