What is the area, in square yards, of the composite shape below?

The shape is made of a rectange and another smaller rectangle conectdd to it. The length if the small rectangle is 3yd the width of the whole shape is 9yd the length of the entire shape is 6yd and the width of the bigger shape is 5yd





Area of a rectangle = lw


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1 answer

To find the area of the composite shape made of two rectangles, we need to clarify the dimensions provided.

  1. Identify the dimensions for the larger rectangle:

    • Length = 6 yards
    • Width = 5 yards
  2. Calculate the area of the larger rectangle: \[ \text{Area}_{\text{larger}} = \text{length} \times \text{width} = 6 , \text{yd} \times 5 , \text{yd} = 30 , \text{yd}^2 \]

  3. Identify the dimensions for the smaller rectangle:

    • Length = 3 yards
    • Width of the whole shape = 9 yards (the width of the smaller rectangle is unknown and implies the overall height must incorporate the smaller rectangle).
  4. Width of the smaller rectangle: Since the width of the whole shape is 9 yards and the width of the larger rectangle is 5 yards, the width of the smaller rectangle can be calculated as: \[ \text{Width}_{\text{smaller}} = 9 , \text{yd} - 5, \text{yd} = 4 , \text{yd} \]

  5. Calculate the area of the smaller rectangle: \[ \text{Area}_{\text{smaller}} = \text{length} \times \text{width} = 3 , \text{yd} \times 4 , \text{yd} = 12 , \text{yd}^2 \]

  6. Total area of the composite shape: \[ \text{Area}{\text{total}} = \text{Area}{\text{larger}} + \text{Area}_{\text{smaller}} = 30 , \text{yd}^2 + 12 , \text{yd}^2 = 42 , \text{yd}^2 \]

Thus, the area of the composite shape is:

\[ \text{Final Answer: } 42 \]