Question:
In Fig. 14.46, the area of ΔABC (in square units) is [CBSE 2013]
(a) 15
(b) 10
(c) $7.5$
(d) $2.5$
Solution:
The coordinates of A are (1, 3).
∴ Distance of A from the x-axis, AD = y-coordinate of A = 3 units
The number of units between B and C on the x-axis are 5.
∴ BC = 5 units
Now,
Area of $\triangle \mathrm{ABC}=\frac{1}{2} \times \mathrm{BC} \times \mathrm{AD}=\frac{1}{2} \times 5 \times 3=\frac{15}{2}=7.5$ square units
Thus, the area of ∆ABC is 7.5 square units.
Hence, the correct answer is option C.