Question

Need help GET BRAINLISTS #8

Answer 1

Answer: 6.7 mm

Step-by-step explanation:

The area of a square is equal to side(side), but is also equal to 1/2(apothem)(perimeter).

The apothem is the perpendicular distance from the center of the square to the midpoint of its side.

We can use these formulas to find the apothem and use the pythagorean theorem to find the hypotenuse (slant height).

Area of square = 9(9) = 81

Area of square = 1/2(apothem)(perimeter)

Perimeter = 4(9) = 36

81 = 1/2(apothem)(36)

162 = apothem(36)

apothem = 4.5

Pythagorean theorem: $a^{2} + b^{2} = c^{2}$

Plug the apothem and the given height into the equation:

$4.5^{2} + 5^{2} = x^{2}$ (x being the slant height)

20.25 + 25 = $x^{2}$

x = $\sqrt{45.25}$

x ≈ 6.7