Question

4 cm
4 cm
7. In the adjoining figure, ABCD is a trapezium
in which AB|| DC; AB = 7 cm; AD = BC = 5 cm
and the distance between AB and DC is 4 cm.
Find the length of DC and hence, find the area
of trap. ABCD.
5 cm
wc
A
7 cm
8​

Answer 1

Answer:

Kindly see the attached diagram.

According to the question, DC = 4cm, AB = 7cm, BC = 5cm, AD = 5cm

From the diagram, AB = AX + XY + YB

XY = DC = 4cm

AX = BY

=> AB = AX + DC + AX (as BY = AX)

=> 7 = 2AX + 4

=> AX = (7 - 4)/2

=> AX = 3/2 = 1.5cm

By Pythagoras theorem, AX² + DX² = AD²

=> (1.5)² + DX² = 5²

=> DX² = 25 - 2.25

=> DX² = 22.75

=> DX = √22.75 = (√91)/2

Area of a Trapezium = (1/2)(a+b)h

From the diagram, a = DC, b = AB, h = DX

=> Area = (1/2)(4 + 7)((√91)/2)

= 11√91/4

≈ 26.233cm²

P.S: That's the best I could do, without being given a figure.....