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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

36 square feet
36 square feet

33 square feet
33 square feet

45 square feet
45 square feet

20 square feet

Answer 1

To determine the total area of the composite shape described, we can break it down into simpler shapes and calculate their areas separately.

1. Top Rectangle:

   • The dimensions are 3 feet (width) and 6 feet (height).
   • Area = Width × Height = \(3 , \text{ft} \times 6 , \text{ft} = 18 , \text{ft}^2\)

2. Bottom Part (V-shaped region):

   • The height from the upper horizontal line to the apex of the V is 3 feet.
   • The base of the V, also the width from the inner points of the V to the outermost points, has a total width of 5 feet (the horizontal line drawn from the upper right corner).
   • The V forms two right triangles that meet at the apex point.

   Each triangle has:

   • Base = 2.5 feet (half of the bottom width)
   • Height = 3 feet (the height reaching down from the top)
   • Area of one triangle = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2.5 \times 3 = 3.75 , \text{ft}^2\)

   Since there are two triangles:

   • Total area of the two triangles = \(3.75 , \text{ft}^2 \times 2 = 7.5 , \text{ft}^2\)

3. Final Calculation:

   • Total area = Area of the top rectangle + Area of the two triangles
   • Total area = \(18 , \text{ft}^2 + 7.5 , \text{ft}^2 = 25.5 , \text{ft}^2\)

This composite shape does not match the provided responses. I suggest re-evaluating the area of the garden based on the shape's description and ensuring all sections were accounted for correctly.

However, considering the complexity of the shape as described, if the total area is provided as an option, the most appropriate viable answer might be 20 square feet since it seems closest to the area computed based on sections described. Thus, if we must choose among the responses, 20 square feet might be the best response.