Question

Calculate the area of quadrilateral ABCD in which ∆ BCD is equilateral triangle with each side equal to 26 CM, angle BAD = 90° and AD = 24 cm​

Answer 1

GIVEN :

• ANGLE BCD IS EQUILATERAL TRIANGLE

• EACH SIDE = 26 CM

• ANGLE BAD = 90°

• AD = 24 CM

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TO FIND :

=> The area of quadrilateral ABCD = ?

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Step - by - step explaination :

In ∆ ABD,

=> AB² + AD² = DB²

=> AB² + (24)² = (26)²

=> AB² + 576 = 676

=> AB² = 676 – 576

=> AB² = 100

=> AB = 10

Area of quadrilateral ABCD = area of ∆DAB + area of ∆DCB

$= > \frac{1}{2} \times ab \times ad + \frac{ \sqrt{3} }{4} \times {db}^{2}$

$= > \frac{1}{2} \times 10 \times 24 + \frac{ \sqrt{3} }{4} \times {(26)}^{2}$

$= > 120 + 169 \sqrt{3} = 120 + 169 \times 1.732$

$= > 120 + 292.37 = 412.37 {cm}^{2}$

The area of parallelogram ABCD =

4.1237 cm²

Answer 2

Step-by-step explanation:

Hello (◔‿◔)

Question:-

Calculate the area of quadrilateral ABCD in which ∆ BCD is equilateral triangle with each side equal to 26 CM, angle BAD = 90° and AD = 24 cm

Answer:-

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

hope it's help

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