Question

The pareallel sides of a trapezium are 25cm and 13 cm and its non-parallel
sides are 10cm each. Find the area of the trapezium.
एक समलंब चतुर्भुज की समातर भुजाएं 25 सेमी और 13 सेमी हैं। इसकी प्रत्येक असमांतर
भूजा 10 सेमी लंबी हैं। समलंब चतुर्भुज का क्षेत्रफल ज्ञात कीजिए।​

Answer 1

Let us say, AB and CD are parallel to each other where,

AB = 13 cm

CD = 25 cm

AC = BD = 10cm (non parallel sides)

Let's make AE parallel to BD

So, AE = BD = 10cm

Now, In triangle ACE,

AC = 10cm = a

CE = 25-13 = 12cm = b

AE = 10cm = c

and, AM is perpendicular at CE.

So, Semiperimeter of ACE =

Sum of sides ÷ 2

$\frac{10 + 12 + 10}{2} \\ \\ \frac{32}{2} \\ \\ s = 16cm \\ \\ area \:of \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{16(16 - 10)(16 - 12)(16 - 10)} \\ \\ \sqrt{16 \times 6 \times 4 \times 6} \\ \\ \sqrt{2304} \\ \\ area \: = 48 {cm}^{2}$

As we know that,

Area of triangle = 1/2×base×height

Here, base = 12cm

and height = AM = ?

So, 1/2×12×h = 48

6h = 48

h = 48÷6

h = 8cm

So, height of ACE = 8cm

This means height of trapezium ABCD is also 8cm

So, Area of trapezium = 1/2(sum of parallel sides)h

= 1/2(25+13)8

1/2 × 38 × 8

38 × 4 = 152cm^2