Use the image to answer the question. 1 ft. 8 ft. 4 ft. 4 ft. 2 ft. 5 ft. 2 ft. Jenny is painting her little brother's wall with a rocket ship design. How much area does the rocket ship design take? (4 points)

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To calculate the area of the rocket ship design you would typically break it down into simpler shapes like rectangles and triangles, based on the dimensions provided:

  1. The rocket ship seems to be composed of multiple sections. Each section's area can be computed using its respective dimensions.
  2. You have given dimensions including 1 ft, 8 ft, 4 ft, 4 ft, 2 ft, 5 ft, and 2 ft, which correspond to different sections of the rocket ship.

Let’s assume the design consists of:

  • A rectangle at the bottom (width: 4 ft, height: 8 ft)
  • A triangle on top for the tip of the rocket (base width: 4 ft, height: 5 ft)
  • Two small rectangular fins at the sides (each 2 ft wide and 4 ft high)

Calculations:

  1. Area of the Rectangular Body: \[ \text{Area} = \text{width} \times \text{height} = 4 , \text{ft} \times 8 , \text{ft} = 32 , \text{sq ft} \]

  2. Area of the Triangular Tip (\( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \)): \[ \text{Area} = \frac{1}{2} \times 4 , \text{ft} \times 5 , \text{ft} = \frac{20}{2} = 10 , \text{sq ft} \]

  3. Area of the Fins (Assuming 2 fins each with area): \[ \text{Area of one fin} = \text{width} \times \text{height} = 2 , \text{ft} \times 4 , \text{ft} = 8 , \text{sq ft} \] \[ \text{Total Area of Fins} = 2 \times 8 , \text{sq ft} = 16 , \text{sq ft} \]

Total Area:

\[ \text{Total Area} = \text{Area of Rectangle} + \text{Area of Triangle} + \text{Area of Fins} \] \[ = 32 , \text{sq ft} + 10 , \text{sq ft} + 16 , \text{sq ft} = 58 , \text{sq ft} \]

Thus, the total area that the rocket ship design takes is 58 square feet.

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