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Upper primary school mathematics question UPQ98
The figure above shows a square ABCD of side 12 cm. Given that AE = CE and BF = CF. Find (a) ∠ EBF and (b) the area of the shaded part.
Since ABCD is a square, ∠ ABC = 900
AE = CE and BF = CF, E is the centre point of the square ABCD
Hence BE is the bi-sector of ∠ ABC
∠ EBF = 900 ÷ 2 = 450
By adding dotted lines as shown in the above diagram
The square ABCD is divided into eight equal portions in term of area
The area of the square ABCD = 12 × 12 = 144cm2
The area of the shaded part = 144 ÷ 8 = 18cm2