Walter made a kite that was in the shape of a rhombus. The height of the kite is 1.5 feet. The length of the base of the kite is 2.2 feet. Find the perimeter and the area of the kite.

The perimeter of the kite is
  
ft.
ft squared .

The area of the kite is

1 answer

To find the perimeter and area of a kite, we can use the properties of a rhombus since a kite is essentially a special type of rhombus.

Given:

  • Height (h) = 1.5 feet
  • Length of the base (b) = 2.2 feet

Perimeter Calculation:

For a kite, the perimeter (P) is given by the sum of all four sides. A kite has two pairs of equal-length sides. If the length of the bases (the two longer sides) is given as 2.2 feet, assume there are shorter sides of equal length.

Since the shape is a rhombus, each side length \(s\) is equal. Thus:

  1. The two longer sides each are 2.2 feet.
  2. To find the lengths of the other sides, we recognize that the area of the kite can also be calculated using the diagonals.

Using the formula for the area of the rhombus given linear algebraic conditions: \[ \text{Area} = \text{base} \times \text{height} = b \times h = 2.2 \times 1.5 = 3.3 \text{ ft}^2 \]

From this, we can use the property of kites that they consist of diagonals overlapping at right angles or calculate the side length directly if necessary.

However, given the base is known across this height and for simplicity, and if we denote s as the side length opposite the base vertically:

Assuming the kite as symmetrical and that the two sides opposite the height are essentially at angle to form a triangle. We can't find just using the base; hence we need the side directly or the terms need this shadow concept.

Given more information regarding the sides is required.

Area Calculation:

The area \(A\) of a kite is calculated as: \[ A = \frac{1}{2} \times d_1 \times d_2 \] However, without specific lengths for the diagonals \(d_1\) and \(d_2\), we can use the area we confirmed earlier from basic height and base interactions.

Conclusion:

Based purely on height and the provided base length:

  • Perimeter calculation will depend on missing dimensions.
  • Area is confirmed as: \[ \text{Area} = 3.3 \text{ ft}^2 \]

To find the perimeter, unfortunately, you also need diagonal lengths or the sides beyond just height and the base dimension. If those come available, the calculations for sides would be:

Perimeter = 2*(side_length_1) + 2*(side_length_2)

Please provide any additional measurement specifics available for proper completion.