11. The base of a parallelogram is half its height. The base measures \( 6 \frac{1}{2} \) inches. Find the area of the parallelogram in square inches.

To find the area of the parallelogram, we use the formula for area: \[ \text{Area} = \text{Base} \times \text{Height} \] Given that the base is \( 6 \frac{1}{2} \) inches, we first convert this mixed number to an improper fraction: \[ 6 \frac{1}{2} = \frac{13}{2} \text{ inches} \] According to the problem, the base is half of its height. If we let the height be \( h \), then: \[ \text{Base} = \frac{1}{2} h \] We know the base is \( \frac{13}{2} \) inches, leading to the equation: \[ \frac{1}{2} h = \frac{13}{2} \] From this, we can solve for \( h \): \[ h = 13 \text{ inches} \] Now we can find the area: \[ \text{Area} = \text{Base} \times \text{Height} = \frac{13}{2} \times 13 \] Calculating this gives: \[ \text{Area} = \frac{169}{2} = 84.5 \text{ square inches} \] So, the area of the parallelogram is \( 84.5 \) square inches.