The Palace of Peace and Accord in Astana, Kazakhstan, was built in 200620062006. The building has a square right pyramid structure. The length of a side of the square base is 62\,\text{m}62m62, start text, m, end text, and the vertical height of the pyramid is also 62\,\text{m}62m62, start text, m, end text.

What is the height, hhh, of one of the triangular faces?

Round your answer to the nearest tenth.

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!

Use pythagorean’s theorem and find the missing side lengths of the two smaller triangles and add them together
13^2 - 12^2 = 5
15^2 - 12^2 = 9
5+9 = 14
14 is the length of each side of the square
14^2 + 14^2 = 19.8
19.8 is the diagonal length of the inside if the square