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WAEC Mathematics 2025 Paper

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Question : 22

Total: 50

The diagonals AC and BD of a rhombus ABCD are 16 cm and 12 cm long, respectively. Calculate the area of the rhombus.

96 cm $^2$
36 cm $^2$
48 cm $^2$
24 cm $^2$

Solution:

Given that AC = 16 cm and BD = 12 cm. If O is the center. The diagonals of a rhombus meet at 90º.

AO =

\frac{\text{AC}}{2}

= 8cm;

BO =

\frac{\text{BD}}{2}

= 6 cm

AB

^2

= AO

^2

+ OB

^2

(pythagoras theorem)

AB

^2

= 64 + 36 = 100;

AB = 10 cm

Area of △ABO =

\frac{1}{2}

× 8 × 6 = 24 cm

^2

Area of rhombus = 4 × area of △ABO ⇒ 4 × 24 = 96 cm

^2

.

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