Question number 24 both parts please explain step by step on a paper

Question number 24 both parts please explain step by step on a paper In the figure (ii) given below, OAB is a quadrant of a circle. radius OA cm and OD 4 cm. Calculate the area of the shaded portioru 2 A student takes a rectangular piece of paper 30 cm long and 21 cm wide. Find the area of the biggest circle that can be cut out from the paper, Also find the area of the paper left after cutting out the circle. A rectangle with one side 4 cm is inscribed in a circle of radius 2•5cm. Find the area Of the rectangle. 24 (a) In the figure 0) given below, calculate the area of the shaded region correct to two decimal places. (Take = 3.142). (b) In the figure given ABC is an isosceles right angled triangle With ZABC 900_ A semicircle is drawn with AC as diameter. If AB = BC = 7 cm. find the area of the shaded region. Take = A circular field has perimeter 660 m. A plot in the shape of a square having its veruc• on the circumference is marked in the field. Calculate the area oi the square field, In the adjoining figure, ABCD is a square. Fund the ratio between 'i) the circumferences 'u' areas of the incircle and the circumcircle oi the

Dear Student,

Answer 24(a):
Diagonal of the rectangle acts as the diameter of circle.And diagonal = 52+122 (Using pythagoras theorem)=25+144=169=13 So the diameter of circle=13 cmThen, its radius=132 cmSo, area of circle=πr2=3.142×132×132=132.75 cm2And area of rectangle=Length × Breadth = 5×12=60 cm2So area of shaded region=area of circle-area of rectangle=132.75 cm2-60 cm2=72.75 cm2

Answer 24(b) :

ABC is a right isosceles triangle.AC2 = AB2 + BC2AC2 =72 + 72AC2 = 49 + 49AC2 = 98AC = 98 = 72 cmSo, diameter of semicircle =  72 cmRadius of semicircle = Diameter2 = 722 cm Area of semicircle =  πr22 = 12 × 227 × 722 × 722 = 772 cm2Area of ABC = 12×Base×Height = 12×BC×AC = 12×7×7 = 492 cm2Area of shaded region = Area of semicircle - Area of ABC = 772 - 492 = 282 = 14 cm2


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