Questions: Quadrilateral J K L M is a kite with an area of 63 square feet. What is the length of NM? A 6 ft B 9 ft C 5 ft D 7 ft

Solution Steps

The problem states that quadrilateral JKLM is a kite with an area of 63 square feet. We need to find the length of NM.

The area \( A \) of a kite 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.

From the diagram:

• One diagonal \( JL \) is given as \( 7 + 7 = 14 \) feet.
• The other diagonal \( KM \) is split into two parts: \( KN = 3 \) feet and \( NM \) (which we need to find).

Using the area formula: \[ 63 = \frac{1}{2} \times 14 \times (3 + NM) \]

First, simplify the equation: \[ 63 = 7 \times (3 + NM) \] \[ 63 = 21 + 7 \times NM \] Subtract 21 from both sides: \[ 42 = 7 \times NM \] Divide by 7: \[ NM = 6 \]

Final Answer