Question

find the area of quadrilateral ABCD in which a b is equal to 24 cm, angle b a d is equal to 900 cm and b, c and the form an equilateral triangle of side 26 CM​

Answer 1

Step-by-step explanation:

The area of quadrilateral ABCD is 412.76 cm²

Step-by-step explanation:

Step 1 : Quadrilateral ABCD forms two triangles.

Equilateral triangle BCD with sides 26 cm and right angled triangle BAD with base 24 cm and hypotenuse 26 cm.

Step 2 : Using Pythagoras theorem get the height AB of the right angled triangle and the height of the Equilateral triangle.

AB = Square root of (BD² - AD²)

= Square root of (676 - 576)

= square root of 100 = 10 cm

Height of the Equilateral triangle :

Height = square root of (26² - (26/2)²)

= Square root of (507) = 22.52 cm

Step 3 : Calculate the area of the two triangles.

Area of a triangle = ½b × h

Area of the right angled triangle = ½ × 24 × 10 = 120 cm²

Area of the Equilateral triangle = ½ × 26 × 22.52 = 292.76 cm²

Step 4 : Sum the two areas to get the total area which is the area of quadrilateral ABCD.

292.76cm² + 120 cm² = 412.76 cm²

Answer 2

It is given that

ABCD is a quadrilateral in which ∠BCA = 900 and AB = 13 cm

ABCD is an equilateral triangle in which AC = CD = AD = 12 cm

In right angled △ABC

Using Pythagoras theorem,

AB2 = AC2 + BC2

Substituting the values

132 = 122 + BC2

By further calculation

BC2 = 132 – 122

BC2 = 169 – 144 = 25

So we get

BC = √25 = 5 cm

We know that

Area of quadrilateral ABCD = Area of △ABC + Area of △ACD

It can be written as

= ½ × base × height + √3/4 × side2

= ½ × AC × BC + √3/4 × 122

Substituting the values

= ½ × 12 × 5 + √3/4 × 12 × 12

So we get

= 6 × 5 + √3 × 3 × 12

= 30 + 36√3

Substituting the value of √3

= 30 + 36 × 1.732

= 30 + 62.28

= 92.28 cm2

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