Question

Prove that the area of triangle is half of the product of its Base and corresponding height.

Answer 1

CP parallel to BA (By Construction)
AP parallel to BC (By Construction)
Therefore BCPA is a parallelogram.
Hence AC is a diagonal of parallelogram BCPA.
Therefore, area of triangle = ½ ar(IIgm BCPA) = ½ × BC × AD (As BC is the base and AD is the altitude of IIgm BCPA).

Answer 2

Answer:

follow the explanation part

Step-by-step explanation:

Let base and height of a parallelogram be a and b respectively. We know that the area A of a parallelogram is A = bh.

Now draw a diagonal to form two congruent triangles within the parallelogram. Now shade one of the triangles, which represents the area t of the triangle. We see that this triangle has base b and height h as well. If we shade the other triangle with base b and height h, we get the total area of the parallelogram.

Since there are two triangles with equal area t, we have

area of triangle * 2 = area of parallelogram

2t = bh or t = 1/2*bh

We see that the area of a triangle is one half the base times the height.