Let square side be s. Two semicircles have total area 2 x (1/2) x π(s/2)² = (1/4)πs², identical to the quarter circle’s area (1/4)πs². Subtracting their common overlapping region proves Area(A) = Area(B).
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Each circle of diameter d sits in a square cell of area d². The ratio of circle area to each cell is (π / 4)d² / d² = π / 4. Both figures have covered fraction π / 4 approximately ...
Diagonals d1 and d2 cross perpendicularly. (i) Algebraically, the kite splits into two triangles on base d1 with heights summing to d2, giving area (1/2)d1d2. (ii) Geometrically, enclosing it in a d1 x d2 rectangle doubles its area.
Yes, they are congruent. Same perimeter gives the same sum of sides and same area gives the same product. They share the identical quadratic equation, producing the exact same side lengths.
Way 1: Since 7² + 24² = 49 + 576 = 625 = 25², it is a right triangle, so Area = (1/2) x 7 x 24 = 84 cm². Way 2: Semi-perimeter s = 28 cm; Heron’s formula yields ...