15. A trapezoid with base measures of(23 km)and 29 km)has an area of 390km^2 Find the height of the trapezoid.

To find the height of the trapezoid, we can use the formula for the area of a trapezoid:<br /><br />\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \]<br /><br />Given:<br />- Base 1 (\( \text{Base}_1 \)) = 23 km<br />- Base 2 (\( \text{Base}_2 \)) = 29 km<br />- Area = 390 km²<br /><br />We need to find the height (\( \text{Height} \)).<br /><br />Substitute the given values into the formula:<br /><br />\[ 390 = \frac{1}{2} \times (23 + 29) \times \text{Height} \]<br /><br />First, simplify the expression inside the parentheses:<br /><br />\[ 390 = \frac{1}{2} \times 52 \times \text{Height} \]<br /><br />Next, multiply 52 by \( \frac{1}{2} \):<br /><br />\[ 390 = 26 \times \text{Height} \]<br /><br />Now, solve for the height by dividing both sides of the equation by 26:<br /><br />\[ \text{Height} = \frac{390}{26} \]<br /><br />\[ \text{Height} = 15 \]<br /><br />So, the height of the trapezoid is 15 km.