Six Problems on Area and Perimeter

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50 Azim Premji University At Right Angles, March 2022

Problem Corner

1

Keywords: Area; Perimeter; Triangle; Trigonometry; Ratio;

Composition; Decomposition; Dissection

Six Problems on Area and Perimeter

2. The accompanying figure shows a square ABCD inscribed in a circle with centre O. Points, P, Q are situated in the minor arc AB such that AP = PQ = QB. Find the ratio of the areas of AOB and quadrilateral APQB.

Area of ABC= ¹₂ab sin C.

A. RAMACHANDRAN

1. The accompanying figure shows a square ABCD inscribed in a circle with centre O. P is the midpoint of minor arc AB. Find the ratio of the areas of AOB and APB.

The following formula for the area of a triangle could be useful to you in solving the first two problems.

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Azim Premji University At Right Angles, March 2022 51

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A. RAMACHANDRAN has had a longstanding interest in the teaching of mathematics and science. He studied physical science and mathematics at the undergraduate level and shifted to life science at the postgraduate level. He taught science, mathematics and geography to middle school students at Rishi Valley School for two decades. His other interests include the English language and Indian music. He may be contacted at [email protected].

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54"= (BD+BF+DF); 54"=(CD+CF+DF);

54" =(BE+BF+EF); 54"=(CE+CF+EF);

54"= (BD+DG+BG); 54"=(CD+CG+DG);

54"=(BE+BG+EG); 54"=(CE+CG+EG).

/PUF UIBU 54"+54"+54"+54"=54"+54"+54"+54"

4P LOPXJOH BOZ TFWFO 54"T POF DBO PCUBJO UIF SFNBJOJOH 54"

A. RAMACHANDRAN has had a longstanding interest in the teaching of mathematics and science. He studied physical science and mathematics at the undergraduate level and shifted to life science at the postgraduate level. He taught science, mathematics and geography to middle school students at Rishi Valley School for two decades. His other interests include the English language and Indian music. He may be contacted at [email protected].