What is the height of a trapezoid with bases of 10 and 6 and an area of 48?

To find the height of a trapezoid when the lengths of the bases and the area are known, we can use the formula for the area of a trapezoid:

[

\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h

]

where ( b_1 ) and ( b_2 ) are the lengths of the two bases, and ( h ) is the height. In this case, we have:

• ( b_1 = 10 )

• ( b_2 = 6 )

• Area = 48

Substituting the known values into the area formula gives us:

[

48 = \frac{1}{2} \times (10 + 6) \times h

]

Calculating the average of the bases:

[

10 + 6 = 16

]

Now, substituting this back into the equation:

[

48 = \frac{1}{2} \times 16 \times h

]

This simplifies to:

[

48 = 8h

]

To isolate ( h ), we divide both sides by 8:

[