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Question

A composite shape is drawn with rectangular shapes at the top and a downward point at the bottom. Starting in the upper left corner is a horizontal line to the right, measuring 3 feet. A perpendicular line is drawn at a right angle downward 3 feet. A horizontal line is drawn to the right 5 feet. A perpendicular line of unknown length is drawn downward at a right angle and forms the right boundary of the shape. At the end of this line, two lines of equal length are drawn leftward to form a V in the center, with a perpendicular height of 3 feet from the starting point to the inverted apex. The final vertical line is drawn upward from the left ending point of the V and meets the top first line at a right angle. This vertical line is the left boundary of the shape and is 6 feet in length.

Raheem designs the garden below. What is the total area of the garden in square feet?

(1 point)
Responses

45 square feet
45 square feet

33 square feet
33 square feet

20 square feet
20 square feet

36 square feet
36 square feet
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Answer 1

The total area of the garden can be calculated by finding the area of the individual rectangular shapes and the triangle formed by the V shape.

The area of the first rectangle is 3 feet x 3 feet = 9 square feet.
The area of the second rectangle is 5 feet x 3 feet = 15 square feet.
The area of the triangle formed by the V shape is (1/2) x base x height = (1/2) x 5 feet x 3 feet = 7.5 square feet.

Adding all the areas together:
9 square feet + 15 square feet + 7.5 square feet = 31.5 square feet

Therefore, the total area of the garden is 31.5 square feet, which is closest to the given option of 33 square feet.