Question : The lengths of the two parallel sides of a trapezium are 28 cm and 40 cm. If the length of each of its other two sides is 12 cm, then the area (in cm2) of the trapezium is:
Option 1: $312\sqrt{5}$
Option 2: $408\sqrt{3}$
Option 3: $204\sqrt{3}$
Option 4: $504\sqrt{3}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $204\sqrt{3}$
Solution : Let ABCD be a trapezium. AB = 40 cm, CD = 28 cm, and AD = BC = 12 cm. DE and CF are perpendicular to AB. As per symmetry AE = FB = 6 cm In the right-angled triangle CFB $CF^2= BC^2-FB^2$ ⇒ $CF^2=12^2-6^2$ ⇒ $CF^2=144-36= 108$ ⇒ $CF=6\sqrt3$ CF is the height of trapezium. Now, the area of trapezium = $\frac{1}{2}\times$(sum of parallel sides) × height = $\frac{1}{2}\times (40+28)\times 6\sqrt3$ = $\frac{1}{2}\times 68\times 6\sqrt3$ = $204\sqrt{3}$ cm$^2$ Hence, the correct answer is $204\sqrt{3}$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm2, then find the length of each of the parallel sides (in cm).
Question : The area of an isosceles trapezium is 176 cm2 and the height is $\frac{2}{11}$th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is:
Question : In a trapezium ABCD, AB and DC are parallel sides and $\angle ADC=90^\circ$. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm, then the area of the trapezium ABCD is:
Question : From any point inside an equilateral triangle, the lengths of perpendiculars on the sides are $a$ cm, $b$ cm, and $c$ cm. Its area (in cm2) is:
Question : The height of an equilateral triangle is $7 \sqrt{3}$ cm. What is the area of this equilateral triangle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile