Observe the above figure and answer the question.
The area of ABCD is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 59 cm2
The diagonal AC splits ABCD into two right triangles, so the area of ABCD is the sum of their areas, each \(\frac{1}{2}\times\) the two sides that meet at the right angle.
\(AC=\sqrt{6^2+8^2}=10\) cm (triangle ADC, right angle at D)
Area of ADC \(\displaystyle =\frac{1}{2}\times6\times8=24\,\mathrm{cm^2}\)
Area of ACB \(\displaystyle =\frac{1}{2}\times10\times7=35\,\mathrm{cm^2}\) (right angle at C)
Area of ABCD \(=24+35=59\,\mathrm{cm^2}\)