The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

parmen Feb 24, 2024

#1**+1 **

The side length of each of the equilateral triangles is 1.

We see that 2 of such side lengths almost make the side length of the larger square, but there's still a little gap.

Each gap is half of a equilateral triangle, or a 30-60-90 triangle, and the length we want is \(\frac{1}{2}\).

So the side length of the larger square is \(2+\frac{1}{2}=\frac{5}{2}\).

The area is \(({\frac{5}{2}})^{2}=\frac{25}{4}\). __So the area of the larger square is __** 25/4**.

hairyberry Feb 24, 2024