From the given diagram, answer the following questions.
‘AC’ is 23 cm in the adjoining figure. Consider the figure and answer the questions
The area of ΔDBC if DB is a straight line
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 32.5 cm2
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\). Since D, G and B lie on one straight line, DB is the base, and CG, which meets DB at a right angle, is the height.
Base DB \(=\) DG \(+\) GB \(=10+3=13\) cm
Height CG \(=5\) cm
Area of \(\Delta\)DBC \(\displaystyle =\frac{1}{2}\times13\times5=32.5\) cm2
The figure 65 cm2 in Option (2) is \(13\times5\) without the half, the area of a rectangle on the same base.