Question

find the area of a trap, whose parallel sides are 25 cm and 11 cm, it's non parallel sides are 15 cm and 13 cm
???​

Answer 1

Answer:

216 cm²  

Step-by-step explanation:

ABCD is a Trapezium whose sides

AB=25 cm,BC=13 cm,CD=11 cm and DA=15 cm

Now do some construction, Draw a line DE which is parallel to BC. Hence forming a parallelogram  DEBC.

Hence DE=BC

Now for finding the area of trapezium we will add area △DAE to the area of || gm.

Now for area of △DAE

We have to find S first, then use Heron's formula.

S = $\frac{AE+DE+DA}{2}$

  = $\frac{(25 - 11)+13+15}{2}$

  = $\frac{42}{2}$

  = 21

Now, Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

= $\sqrt{21(21 - 15)(21 - 14)(21 - 13)}$

= 84 cm²

Now draw DF  ⊥ to E hence →

Area of △ADE= 1/2 × Base × height

84 cm² = 1/2×14×h

h = 12 cm

Now area of parallelogram =11×12=132 cm²

Area of Trapezium =216 cm²               {i.e,132+84}