Let's solve each problem step by step.
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Area of a square with each side measuring 13 feet: The area of a square is calculated as: \[ \text{Area} = \text{side}^2 \] So, for a square with a side of 13 feet: \[ \text{Area} = 13^2 = 169 \text{ ft}^2 \] Therefore, the correct response is 169 ft. squared.
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Area of a rectangle that is twice as long as it is tall, with height 5 centimeters: If the height is 5 cm and the length is twice the height: \[ \text{Length} = 2 \times 5 = 10 \text{ cm} \] The area is given by: \[ \text{Area} = \text{Length} \times \text{Height} = 10 \times 5 = 50 \text{ cm}^2 \] Therefore, the correct response is 50 cm squared.
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Area of a triangle with base 13 yards and height 5 yards: The area of a triangle is calculated as: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For a triangle with a base of 13 yards and a height of 5 yards: \[ \text{Area} = \frac{1}{2} \times 13 \times 5 = \frac{65}{2} = 32.5 \text{ square yards} \] Therefore, the correct response is 32.5 square yards.
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Finding the height of a triangular sandwich with base 4 inches and area 7 square inches: Using the area formula for a triangle: \[ 7 = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting the base value: \[ 7 = \frac{1}{2} \times 4 \times \text{height} \] Rearranging gives: \[ 7 = 2 \times \text{height} \] \[ \text{height} = \frac{7}{2} = 3.5 \text{ inches} \] Therefore, the correct response is 3.5 inches.
Answers summary:
- 169 ft. squared
- 50 cm squared
- 32.5 square yards
- 3.5 inches