Question

Find the area of an isosceles triangle each of two equal sides being ‘α’ and the angle

included between them 45°.

Please answer without using trigonometry .​

Answer 1

Answer:

Step-by-step explanation:

AB = AC = a

draw a perpendicular bisector from C on side AB.

in Δ ACD,

a² = a²/4 + CD²

4a²-a²/ 4 = CD²

3a²/4= CD²

$\frac{a\sqrt{3}}{2}$ = CD

Area of Δ ABC = 1/2*B*H

                         =  1/2 *a* a√3/2

                         =  $\frac{a^2\sqrt{3}}{4}$

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