Question

find height and area in DX fig

Answer 1

Geometry,

We have,

ABCD parallelogram who's length = 14 units and breadth = 7 units.

Have to find the area.

Now,
Draw a midpoint of AB.Name it point F
Join F and C.
We'll get an equilateral triangle whose sides are 7 units.

As we know that the height of an equilateral triangle = √3/2a [ where a is the sides of equilateral triangle ]
So the height will be √3/2 × 7 = 7√3/2 units.

But this is attached with the parallelogram, so the height of the parallelogram will be also 7√3/2 units.

And the main answer.

The area of the parallelogram = Base × Height
= 14 × 7√3/2 units²

= 49√3 units²

If you are not familiar with the formula then it could be done with another formula.

You know Heron's formula isn't it.

Here S(sum of all sides of a triangel/2) = (7× 3)/2
As we know,
$\sqrt{s(s - a)(s - b)(s - c)}$
where a,b andc are the sides of triangle
although here all sides are equal (a = b = c = 7)

= √{21/2(21/2 - 7)(21/2 - 7)(21/2 -7)}

= √(21/2 × 7/2 × 7/2 × 7/2)

= √(7/2×3 ×7/2 × 7/2 × 7/2)

= 7/2 × 7/2 √3

= 49/4√3 units²

This is the area of the triangle.

Let the height of the triangle = h unit

So, 1/2 × h × 7 = 49/4√3

or, h = 7/2√3 units

Happy now.

That's it
Hope it helped ❤(ӦｖӦ｡)