Question

the length of a parallel side of a trapezium are 25cm and 10 cm and the length of the slant side are 14 and 13cm calculate the area of a trapezium​

Answer 1

Step-by-step explanation:

The area of a trapezium is half the sum of the parallel sides multiplied by the distance between them.

This is easy to demonstrate.

Trapezium area = area of triangle ABF + area of triangle CDE + area of rectangle BCEF

= 0.5xh + 0.5(15-x)h + 10h = 17.5h = 0.5(10+25)h

So, what is h ?

Let’s use our old friend Pythagoras:

1: Triangle ABF: 132=x2+h2

2: Triangle CDE: 142=(15−x)2+h2=225−30x+x2+h2

Using 1., we can substitute 169 (= 132 ) for x2+h2 , giving us:

196=225−30x+169⇒30x=225+169−196=198

⇒x=6.6⇒x2=43.56

Substituting this into 1 and we have:

169=43.56+h2⇒h2=169−43.56=125.44

⇒h=11.2

Area=17.5h=17.5×11.2=196

Answer: Area is 196 sq. cm

Answer 2

Answer:

To calculate area we need perpendicular distance between two parallel lines.

since slant sides are different, drop normal from side 10 on side 25. 15cm will remain.

Then let on side 14, x be the part out of 15

then the part on the side 13 will be 15-x

now two right angle triangles with hypoteneous

14 and 13 having same altitude say h

you have two eq: 14^2=x^2+h^2 and 13^2=h^2+(15-x)^2.

subtract one eq from other you will get value of x=8.4

Substitute this value of x in one above eq. you will get value of h=11.2

Now area=((10+25)/2)×11.2=196Ans