Real-Life Polynomial Problems: Area and Volume Challenges

A rectangular garden has a length of (2x + 3) meters and a width of (x + 4) meters. What is the area of the garden in terms of x?

• 2x^2 + 8x + 12

• 2x^2 + 7x + 12

• x^2 + 11x + 12

• 2x^2 + 11x + 12

A box has a length of (x + 5) cm, a width of (2x - 1) cm, and a height of (3x + 2) cm. What is the volume of the box expressed as a polynomial?

• 6x^3 + 31x^2 + 3x - 10

• 7x^3 + 30x^2 - 3x + 12

• 4x^3 + 25x^2 + 2x + 1

• 5x^3 + 20x^2 + 15x - 5

A farmer wants to plant two types of crops in a field. The first crop occupies an area represented by (x^2 + 2x) square meters, and the second crop occupies (3x + 4) square meters. What is the total area occupied by both crops?

• x^2 + 2x + 3

• 3x^2 + 4x

• x^2 + 3x + 4

• x^2 + 5x + 4

A rectangular swimming pool has a length of (3x + 2) meters and a width of (x + 1) meters. If the pool is surrounded by a deck that is 2 meters wide, what is the area of the deck in terms of x?

• x^2 + 5x + 12

• 2x^2 + 8x + 18

• 3x^2 + 6x + 15

• 4x^2 + 10x + 20

A rectangular poster has a height of (x + 3) inches and a width of (2x + 1) inches. If the poster is framed with a border that is 1 inch wide, what is the area of the framed poster?

• 2x^2 + 10x + 12

• x^2 + 6x + 8

• 3x^2 + 15x + 20

• 2x^2 + 13x + 15

A classroom has a length of (4x - 2) feet and a width of (x + 5) feet. If the school plans to add a new section that is (2x + 3) feet long and (x + 1) feet wide, what will be the total area of the classroom and the new section?

• 5x^2 + 20x - 5

• 6x^2 + 23x - 7

• 4x^2 + 15x - 3

• 7x^2 + 25x - 10

A rectangular plot of land has dimensions of (x + 6) meters by (2x - 3) meters. If a fence is built around the plot, what is the polynomial expression for the perimeter of the plot?

• 4x + 6

• 2x + 3

• 8x - 3

• 6x + 6

A rectangular piece of fabric has a length of (5x + 1) yards and a width of (3x - 2) yards. If the fabric is cut into smaller pieces that are (x + 1) yards long and (2x - 1) yards wide, how many pieces can be cut from the fabric?

• 5

• 10

• 3

• 7

A rectangular aquarium has a length of (2x + 4) feet, a width of (x + 2) feet, and a height of (3x + 1) feet. What is the total surface area of the aquarium?

• 2(3x^2 + 10x + 5) = 6x^2 + 20x + 10

• 2(5x^2 + 15x + 8) = 10x^2 + 30x + 16

• 2(2x^2 + 8x + 4 + 6x^2 + 14x + 4 + 3x^2 + 5x + 2) = 2(11x^2 + 27x + 10) = 22x^2 + 54x + 20

• 2(4x^2 + 12x + 6) = 8x^2 + 24x + 12

A rectangular field has a length of (x^2 + 3x) meters and a width of (2x + 5) meters. If the field is divided into two equal parts, what is the area of each part in terms of x?

• x^3 + (11/2)x^2 + (15/2)x

• (x^2 + 3x)(2x + 5)

• x^3 + 6x^2 + 15x

• x^3 + 5x^2 + 10x