if ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm if AD=2âˆš5,find the area - Maths - Areas of Parallelograms and Triangles

Question

if ABCD is a rectangle inscribed in a quadrant of a circle
of radius 10cm if AD=2 âˆš5,find the
area of the retangle

Vimala · Accepted Answer

Consider the following figure

In the above figure, the rectangle ABCD is inscribed in a quadrant of the circle The radius of the circle, AC is given as AC = 10 cm Also given that $A D = 2 \sqrt{5} c m$ We need to find the area of the rectangle ABCD Consider the right triangle ACD Thus by Pythagorean Theorem, we have $A C^{2} = A D^{2} + C D^{2} 10^{2} = {(2 \sqrt{5})}^{2} + {C D}^{2} 100 = 4 \times 5 + {C D}^{2} {C D}^{2} = 100 - 20 {C D}^{2} = 80 C D = \sqrt{80} C D = 4 \sqrt{5}$ Area of the recatangle ABCD is the product of its length and width Thus, $a r (A B C D) = A B \times A D = 4 \sqrt{5} \times 2 \sqrt{5} = 40 s q c m$ Thus the area of the rectangle ABCD is 40sq cm

if ABCD is a rectangle inscribed in a quadrant of a circle of radius 10cm. if AD=2 √5,find the area of the retangle.