Question

question 15 (multiple choice worth 2 points) (areas of triangles, quadrilaterals, and composite figures mc) a community has an empty field ready for development and plans to place a playground in the center. a model of the plan for the project is shown. how much area is left for development in the field outside the playground? options: 756 ft², 576 ft², 288 ft², 180 ft²

Explanation:

Step1: Calculate area of large rectangle

The formula for the area of a rectangle is \( A = l \times w \). For the large rectangle, \( l = 36 \) ft and \( w = 21 \) ft. So, \( A_{large} = 36 \times 21 \).
\( 36 \times 21 = 756 \) square feet.

Step2: Calculate area of playground (small rectangle)

For the small rectangle (playground), \( l = 15 \) ft and \( w = 12 \) ft. Using the area formula, \( A_{playground} = 15 \times 12 \).
\( 15 \times 12 = 180 \) square feet.

Step3: Subtract playground area from large area

To find the area left for development, subtract the area of the playground from the area of the large rectangle: \( A_{development} = A_{large} - A_{playground} \).
\( A_{development} = 756 - 180 = 576 \) square feet.

Answer:

576 ft²