Questions: 2√2 2√2 8√2 9√2

Solution Steps

The given shape is a composite figure consisting of a larger rectangle with a smaller rectangle subtracted from the top. The dimensions provided are:

• Height of the larger rectangle: \(8\sqrt{2}\)
• Width of the larger rectangle: \(9\sqrt{2}\)
• Height of the smaller rectangle: \(2\sqrt{2}\)
• Width of the smaller rectangle: \(2\sqrt{2}\)

The area of a rectangle is given by the formula: \[ \text{Area} = \text{Height} \times \text{Width} \] For the larger rectangle: \[ \text{Area}_{\text{large}} = 8\sqrt{2} \times 9\sqrt{2} \] \[ \text{Area}_{\text{large}} = 72 \times 2 \] \[ \text{Area}_{\text{large}} = 144 \]

For the smaller rectangle: \[ \text{Area}_{\text{small}} = 2\sqrt{2} \times 2\sqrt{2} \] \[ \text{Area}_{\text{small}} = 4 \times 2 \] \[ \text{Area}_{\text{small}} = 8 \]

To find the area of the composite shape, subtract the area of the smaller rectangle from the area of the larger rectangle: \[ \text{Area}_{\text{composite}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} \] \[ \text{Area}_{\text{composite}} = 144 - 8 \] \[ \text{Area}_{\text{composite}} = 136 \]

Final Answer