in figure DE | BC. DE = 3 cm, BC = 9 cm and or (AADE) = 30 cm? Find ar (trap bced)
Answers
Answer:
area of trapezium BCED = 10/3
Step-by-step explanation:
in tri ADE and tri ABC
angle A = angle A(common angle)
angle ADE = angle ABC(corresponding angles as DE//BC)
tri ADE ~(similar to) tri ABC (by A.A test)
AD/AB = DE/BC = AE/AC [corresponding sides of the similar triangles are in proportion]
so DE/BC is an corresponding sides
the theorem which will be used here is :
theorem is : the ratio of the areas of polygon is equal to the ratio of the squares of the corresponding sides.
area of trapezium BCED / area of tri ADE = BC^2/DE^2 [by theorem]
[area of trapezium BCED = area of tri ABC - area of tri ADE]
area of trapezium BCED / area of tri ADE = 3^2/9^2
area of trapezium BCED / area of tri ADE = 9/81
[area of tri ADE = 30cm]
area of trapezium BCED / 30 = 9/81
area of trapezium BCED = 9*30/81 => 30/9 = 10/3
area of trapezium BCED = 10/3
hope it helps!
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