Question

hey! ya better explain to get brilliant answer

Answer 1

Geometry,

Here we have

AB||CD
and AB = 78 cm
CD = 52 cm
BC = 30 cm
AD = 28 cm

Now we'll draw a line CE (not present in the picture,sorry) parallel to AD ,as in the picture above.

So,CE will also be 28 cm .

Now we have two figures one triangle BCE and one parallelogram AECD.

Now area of the triangle =
$\sqrt{s(s - a)( s- b)( s- c)}$
Where s = sum of the three sides divided by two[(a + b + c)/2].And a, b and c are the sides of the triangle.

Now,
a = 30 ,b = 28 and c = 26
s = (30 + 28 + 26)/2 = 42

So the area,
$\sqrt{42(42 - 30)(42 - 28)(42 - 26) } \\ \sqrt{42 \times 12 \times 14 \times 16 } \\ \sqrt{336 \times 336} \\ 336 \: cm$
Now we have area = 336 cm
and base as 26 cm
let the height as h
so,½ × h × 26 = 336
or, h = 336/13 cm

Also the height of the parallelogram is 336/13 cm
As we know that area of the parallelogram = Side × height
= 336/13 × 52 cm²

= 336 × 4 cm²

which is 1344 cm²

Now the area of the trapezium = area of the triangle + area of the parallelogram.
= (336 + 1344) cm²

= 1680 cm²

That's it
Hope it helped (๑´•.̫ • `๑)