Question

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 1

Step-by-step explanation:

According to the above quardilateral

AO=8M

OC=10M

BD= 40m

area= ?

in , ABD

area of triangle =1/2x40x8

=80 m2

in, BDC

area of triangle = 1/2x10x40

=200m2

hence, are of quadrilateral = 200+80

=280m 2

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Answer 2

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

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★ 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 .