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find the area and perimeter of quadrilateral ABCD

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Ramesh answered 3 year(s) ago

Find the area of the quadrilateral ABCD.

In the quadrilateral ABCD, ∠BAD = 90° and ∠BDC = 90°, All measurements are in centimetres. Find the area of the quadrilateral ABCD, where AB = 6 cm, AD = 8 cm and BC = 26 cm.

Class-VIII Maths

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Asked by Shankar kumar

Aug 24

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Ramesh , SubjectMatterExpert

Member since Apr 01 2014

Sol:


According to Pythagoras theorem, BD2= AB2 + AD2

⇒ BD2 = 62 + 82
⇒ BD2 = 36 + 64
⇒ BD2 = 100
⇒ BD = 10 cm

Area of triangle ABD = 1/2 × base × height
                              = 1/2 × AB × AD
                               = 1/2 × 6 × 8
                               = 24 sq cm

According to Pythagoras theorem, BC2= BD2 + CD2

⇒ 262 = 102 + CD2
⇒ CD2 = 676 - 100
⇒ CD2 = 576
⇒ BD = 24 cm

Area of triangle BDC = 1/2 × base × height
                              = 1/2 × BD × CD
                               = 1/2 × 10 × 24
                               = 120 sq cm

Area of the quadrilateral ABCD = Area of triangle ABD + Area of triangle BDC
                                             = 24 + 120
                                             = 144 sq cm.

Answer 2

Some important information:

Herons formula to calculate area = √{ s ( s - a ) ( s - b ) ( s - c ) }, where a, b and c refers to the sides of the triangle and s refers to the semi perimeter of the triangle which is half the sum of all sides

Area of a right - angled triangle = 1 / 2 * Base * Height ( also called altitude )

In a right angled triangle, according to Pythagoras Theorem, we can say that,
( Hypotenuse ) ^ 2 = ( Base ) ^ 2 + ( Perpendicular ) ^ 2


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