From the given diagram, answer the following questions.
‘AC’ is 23 cm in the adjoining figure. Consider the figure and answer the questions
The total area of figure is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 175.5 cm2
The figure is split by the diagonal AC and the two perpendiculars DB and EF into three triangles and one trapezium, and the total area is the sum of their areas. The only length not marked is GF, which comes from AC.
Missing lengths (AC = 23 cm):
GF \(=23-5-11=7\) cm
GA \(=7+11=18\) cm
Areas of the four parts (each triangle has its height along AC, since DB and EF are perpendicular to it):
Triangle DBC \(\displaystyle =\frac{1}{2}\times13\times5=32.5\) cm2 (DB \(=10+3=13\) cm)
Trapezium DGFE \(\displaystyle =\frac{1}{2}\times(10+9)\times7=66.5\) cm2
Triangle EFA \(\displaystyle =\frac{1}{2}\times9\times11=49.5\) cm2
Triangle GBA \(\displaystyle =\frac{1}{2}\times3\times18=27\) cm2
Total area \(=32.5+66.5+49.5+27=175.5\) cm2.