### Math Notes

Subjects

#### Solid Geometry Solutions

##### Topics || Problems

A vegetable bin built in the form of a cube with an edge of $$6 ~ft$$ is divided by a vertical partition which passes through two diagonally opposite edges. Find the lateral surface of either compartment.

$$LSA = 2A_s + A_d$$, the lateral surface area is the sum of the area of two square sides $$2A_s$$ and the area of the diagonal side $$A_d$$.

Diagonals of a square is $$s\sqrt{2}$$, where $$s$$ is the side.

$$A_s = 6x 6 = 36$$

$$A_d = 6(6\sqrt{2}) = 36\sqrt{2}$$

$$LSA = 2(36) +36\sqrt{2}$$

$$LSA = 122.91~ft^2$$