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 DGFE is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 66.5 cm2
DG and EF are both perpendicular to AC, so they are parallel, and DGFE is a trapezium with these two parallel sides and GF as the distance between them. Area of a trapezium \(=\frac{1}{2}\times(\text{sum of the parallel sides})\times\text{height}\).
Parallel sides: DG \(=10\) cm and EF \(=9\) cm
Height GF \(=\) AC \(-\) CG \(-\) FA \(=23-5-11=7\) cm
Area \(\displaystyle =\frac{1}{2}\times(10+9)\times7=\frac{133}{2}=66.5\) cm2
The figure 133 cm2 in Option (1) is \((10+9)\times7\) before it is halved.