Check up 1 write an expression for the area of the gym. Write an expression for the area of the cafeteria. Write an expression for the total area of the gym and cafeteria. Write an expression for the total perimeter of the gym and cafeteria.

a. The expression for the area of the gym is 15·x

b. The expression for the area of the cafeteria is 15·x + 45

c. The expression for the total area of the gym and the cafeteria is 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria is 36 + 4·x

Step-by-step explanation:

The parameters of the given figures are;

The width of the figure, w = 15

The breadth of the gym, = x

The breadth of the cafeteria, = x + 3

The shape of the area of the gym = A rectangle

The shape of the area of the cafeteria = A rectangle

a. The expression for the area, 'A₁', of the gym is given by the area of a rectangle which is Width × Breadth

The area of the gym, A₁ = The width of the figure × The breadth of the gym

Therefore, we have; The area of the gym, A₁ = w ×

A₁ = 15 × x

The area of the gym, A₁ = 15·x

b. The area of the cafeteria, A₂ = The width of the figure × The breadth of the cafeteria

The area of the cafeteria, A₂ = w ×

∴ A₂ = 15 × (x + 3) = 15·x + 45

The expression for the area of the cafeteria, A₂ = 15·x + 45

c. The expression for the total area of the gym and the cafeteria, 'A', is given as follows;

A = A₁ + A₂

∴ A = 15·x + 15·x + 45 = 30·x + 45

The expression for the total area of the gym and the cafeteria = 30·x + 45

d. The expression for the total perimeter of the gym and the cafeteria, 'P', is given as follows;

P = The perimeter of the rectangular area of the gym plus the area of the cafeteria

∴ P = 2 × 15 + 2 × (x + x + 3)

P = 30 + 4·x + 6

P = 36 + 4·x

The expression for the total perimeter of the gym and the cafeteria P = 36 + 4·x.

what i would say the best answer is a. 40.5