To find the perimeter and the area of the kite that Walter made, let's break it down step by step.
Part 1: Perimeter of the Kite
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Identify the properties of a rhombus: A rhombus has all four sides equal in length.
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Use the information given: We know the height (1.5 feet) and the length of the base of the kite (2.2 feet). The base of the kite in a rhombus refers to the part of the kite that is considered as the part opposite the apex forming the kite's upper part.
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Find the length of a side: The height divides the kite into two right triangles.
- Each triangle has a height of 1.5 feet, and half the base (which is half of 2.2 feet) is \( \frac{2.2}{2} = 1.1 \) feet.
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Use Pythagorean theorem to find the length of a side \( s \): \[ s = \sqrt{(1.1)^2 + (1.5)^2} = \sqrt{1.21 + 2.25} = \sqrt{3.46} \approx 1.86 \text{ feet} \]
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Calculate the perimeter: Since there are 4 equal sides: \[ \text{Perimeter} = 4s = 4(1.86) \approx 7.44 \text{ feet} \]
Part 2: Area of the Kite
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Use the area formula of a kite: The area \( A \) can be calculated using the formula: \[ A = \frac{1}{2} \times d_1 \times d_2 \] where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.
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Find the length of the diagonals: In a rhombus, one diagonal runs horizontally (the base length) and the other runs vertically (the height):
- \( d_1 = 2.2 \) feet (base length)
- \( d_2 = 1.5 \) feet (height)
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Calculate the area: \[ A = \frac{1}{2} \times 2.2 \times 1.5 = \frac{1}{2} \times 3.3 = 1.65 \text{ square feet} \]
Final Answers
- The perimeter of the kite is approximately 7.44 feet.
- The area of the kite is 1.65 square feet.