Question

Given: △AMF
AM=MF=AF=a, KLPS is a square
Find: Area of KLPS

Answer 1

Answer:

5a²/16

Step-by-step explanation:

Given that in Δ AMF

AM=MF=AF= a

KLPS is a square inside the triangle.

As we know that perpendicular from F divide the AM equally,

i.e. AD= a/2

Let K and L be the center point on AF and MF respectively,

AK= a/2

ML= a/2

Let b be the side of square then,

b²= ML²+PM²= (a/2)²+ (a/4)²

a²/4+a²/16

=5a²/16

b²= Area of square= 5a²/16

Answer 2

Answer:

$\frac{3}{7+4\sqrt{3} } a^{2}$