Question 24 - End-of-Chapter Exercises - Chapter 6 Class 9 - Measuring Space: Perimeter and Area (Ganita Manjar

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Question 24 In Fig. 6.52, semicircles have been drawn on all the sides of a right-angled triangle as shown. Show that Area (A) + Area (B) = Area (C). Let’s answer this step by step Problem 24: Semicircles on a Triangle Show that Area . 1 Start with the right-angled triangle. Let's call its area . Its sides are (left), (bottom), and hypotenuse . Problem 24: Semicircles on a Triangle Show that Area Area rea . 2 Draw a semicircle on side . Let's call the area of this entire semicircle Small Semi 1.Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 3 Draw a semicircle on side b. Let's call the area of this one Small Semi 2. Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 4 If we color all of this green, our Total Area is made of three pieces added together: Total Area =( Small Semi +(" Small Semi 2 ")+ Triangle CProblem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 5 Pythagoras' theorem (a^2+b^2 ┤=c^2 ) gives us a neat circle rule: The area of the two small semicircles added together exactly equals the area of a big semicircle drawn on the hypotenuse c. Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 6 Let's draw that big pink semicircle on c. Because it's a right triangle, this large semicircle perfectly covers the entire triangle and part of the small semicircles! Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 7 Look at the green shapes that are NOT covered by the pink semicircle. Those are our Lunes, labeled A and B. Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 8 This means the area of A+B is just whatever is left over from our Total Area after subtracting the big pink semicircle. Area (A)+Area(B)=( Total Area) - (Big Semi)Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 7 Look at the green shapes that are NOT covered by the pink semicircle. Those are our Lunes, labeled A and B. Problem 24: Semicircles on a Triangle Show that Area (A)+ Area (B)= Area (C). 8 This means the area of A+B is just whatever is left over from our Total Area after subtracting the big pink semicircle. Area (A)+Area(B)=( Total Area) - (Big Semi