# In the Below Fig. Abcd is a Trapezium in Which Ab = 7 Cm, Ad = Bc = 5 Cm, Dc = X Cm, and Distance Between Ab and Dc is 4cm. Find the Value of X and Area of Trapezium Abcd. - Mathematics

In the below fig. ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm,
and distance between AB and DC is 4cm. Find the value of x and area of trapezium ABCD.

#### Solution

Draw AL ⊥ DC, BM ⊥ DC Then ,

AL = BM = 4cm and LM = 7 cm

AD2 = AL2 + DL2 ⇒ 25 = 16 + DL2 ⇒ DL= 3 cm

Similarly  MC = sqrt(BC^2-BM^2)=sqrt(25-16)=3cm

∴ x  = CD = CM + ML + CD = 3 + 7 + 3  = 13cm

ar (trap . ABCD ) = 1/2 ( AB + CD) × AL 1/2 (7 + 13) xx 4cm^2

= 4cm2

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 5 | Page 44