perplexus.info :: Geometry : Another triangle in a square problem

Another triangle in a square problem (Posted on 2023-03-29)

ABCD is a square with point E inside the square.
Line segments AE, BE, and DE are drawn.
The length of AE is 8 and angle AEB is a right angle.

What is the area of triangle AED?

See The Solution Submitted by Brian Smith

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Simple trig solution

| Comment 2 of 4 |

Let x be the side length of the square.

cos(∠BAE)=8/x

Cofunctions of complementary angles are equal so

sin(∠DAE)=8/x

Area ΔAED = 1/2*8*x*sin(∠DAE) = 1/2*8*x*8/x = 32

Posted by Jer on 2023-03-29 14:33:56

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