Question

the adjoining figure is a trapezium ABCD. find its area and length of the sides BC and AD.​

Answer 1

Given: A trapezium with side AB =16 cm, AC = 20 cm, CD = 21 cm.

To find: Area of the trapezium and length of the sides BC and AD.​

Solution:

• Now we have given angle ABC = 90 degree.

• So In triangle ABC, applying Pythagoras theorem, we get:

                  AB² + BC² = AC²

                  16² + BC² = 20²

                  BC² = 400 - 256

                  BC² = 144

                  BC = 12 cm

• Now lets say a point Q below D parallel to BC with QD = 12 cm. Then QA = 21 - 16 = 5 cm.

• Now consider the triangle AQD, applying Pythagoras theorem, we get:

                  AQ² + QD² = AD²

                  AD² = 5² + 12²

                  AD² = 25 + 144

                  AD² = 169

                  AD = 13 cm.

• Area of trapezium is :

                  A = (a + b)/2 x h

                  A = ((16+21)/2 x 12

                  A = 37/2 x 12

                  A = 18.5 x 12

                  A = 222 cm²

Answer:

         So the area of trapezium is 222 cm², AD = 13 cm and BC = 12 cm.