Question

A trapezium ABCD has side AD parallel to BC, ∠BAD=90∘, BC=3 cm, and AD=8 cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is

Answer 1

The correct answer is 66:
Given the information:
- Side BC = 3 cm
- Side AD = 8 cm
- Perimeter of the trapezium = 36 cm
Let the other two sides of the trapezium be AB and CD. Since AD is parallel to BC, we have AB = CD.
The perimeter of a trapezium is given by the sum of all its four sides:
Perimeter = BC + CD + DA + AB
Given that BC = 3 cm and AD = 8 cm, we can substitute the values and simplify the equation:
36=3+CD+8+AB
Now, rearrange the equation to solve for AB + CD:
AB+CD=36-(3+8)
AB+CD=25
Since AB=CD, we can write:
2. AB=25
$AB=CD=\text(\frac{25}{2})$
AB=CD=12.5 cm
Now, let's find the height of the trapezium. Since ∠BAD=90°, we can use the Pythagorean theorem:
$BD^2 = AB^2 - AD^2$
$BD^2 = (12.5)^2 - (8)^2$
$BD^2=156.25-64$
$BD^2=92.25$
$BD=\sqrt{92.25}$
BD≈9.61 cm
The area of the trapezium can be calculated using the formula:
Area=$(1/2)\times(sum of parallel sides)\times{height}$
Area = $(1/2)\times(AB+CD)\times{BD}$
Area = $(1/2)\times(12.5+12.5)\times9.61$
Area≈66 square cm
Hence, the area of the trapezium is approximately 66 square cm.