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Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26cm, AD = 24cm and ∠ BAD = 90°. Also, find the perimeter of the quadrilateral. (Given, √3 = 1.73.) |
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Answer» In △ ABD Using the Pythagoras theorem BD2 = AB2 + AD2 By substituting the values 262 =AB2 + 242 On further calculation AB2 = 676 – 576 By subtraction AB2 = 100 By taking out the square root AB = √100 So we get Base = AB = 10cm We know that area of △ ABD = ½ × b × h By substituting the values Area of △ ABD = ½ × 10 × 24 On further calculation Area of △ ABD = 120 cm2 We know that the area of △ BCD = √3/4 a2 By substituting the values Area of △ BCD = (1.73/4) (26)2 So we get Area of △ BCD = 292.37 cm2 So we get area of quadrilateral ABCD = Area of △ ABD + Area of △ BCD By substituting the values Area of quadrilateral ABCD = 120 + 29237 By addition Area of quadrilateral ABCD = 412.37 cm2 The perimeter of quadrilateral ABCD = AB + BC + CD + DA By substituting the values Perimeter = 10 + 26 + 26 + 24 So we get Perimeter = 86cm Therefore, the area is 412.37 cm2 and perimeter is 86cm. 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 4.2 77 votes THANKS 85 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 |
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