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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.

Solution:

Since ABCD is a square, ∠ ABC = 90^{0}

AE = CE and BF = CF, E is the centre point of the square ABCD

Hence BE is the bi-sector of ∠ ABC

∠ EBF = 90^{0} ÷ 2 = 45^{0}

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 = 144cm^{2}

The area of the shaded part = 144 ÷ 8 = 18cm^{2}