In the given figure, area of Isosceles triangle ABE is 72 cm2. If BE = AB, AB = 2AD and AE || DC. Then, what is the area (in cm) of the trapezium ABCD ?
Question
In the given figure, area of Isosceles triangle ABE is 72 cm2. If BE = AB, AB = 2AD and AE || DC. Then, what is the area (in cm) of the trapezium ABCD ?
Solution
The problem doesn't provide a figure, but based on the description, we can infer the following:
-
Triangle ABE is an isosceles triangle, meaning two of its sides are equal. In this case, AB = BE.
-
AB = 2AD. This means that AD is half the length of AB.
-
AE || DC. This means that line AE is parallel to line DC.
-
The area of triangle ABE is 72 cm².
To find the area of trapezium ABCD, we need to find the area of triangle ACD and add it to the area of triangle ABE.
Since AE is parallel to DC and AB = 2AD, triangle ACD is similar to triangle ABE. The ratio of their areas is the square of the ratio of their corresponding sides.
Since AB = 2AD, the ratio of the sides is 2:1. Therefore, the ratio of the areas is 4:1.
This means that the area of triangle ACD is 4 times the area of triangle ABE, which is 4 * 72 cm² = 288 cm².
Finally, the area of trapezium ABCD is the sum of the areas of triangles ABE and ACD, which is 72 cm² + 288 cm² = 360 cm².
Similar Questions
A trapezium ABCD is inscribed in a circle of radius 17 cm. Sides AB and CD are parallel, and the perpendicular distance between them is 23 cm. If AB = 16 cm, then what is the area (in sq. cm) of the trapezium ABCD?
The parallel sides DC and AB of a trapezium are 10 cm and 20 cm respectively. Its non-parallel sides are each equal to 13 cm. Then area of trapezium is
If a triangle and a parallelogram are drawn on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram and Triangles drawn on the same base and between the same parallel lines are equal in area ABCD is a trapezium in which AB∥CD and DC = 40cm and AB = 60cm. If X and Y are respectively the mid-points of AD and BC, ar(trap .DCYX) = p × ar (trap. XYBA). Find the value of p.
An isosceles trapezium is circumscribed about a circle. One of the parallel sides is 1.5 times the other. What is the approximate area of the trapezium, if its perimeter is 24 cm?
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.