A trapezoid has an area of 10.5cm^2 and parallel sides that meausure 5.0cm and 2.0cm. What is the height of the trapezoid? Explain what you did.
To find the height of a trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) × (sum of the parallel sides) × height.
In this case, the area of the trapezoid is given as 10.5 cm², and the parallel sides are 5.0 cm and 2.0 cm. Let's assign variables to the known values:
Area = 10.5 cm²,
Side1 = 5.0 cm,
Side2 = 2.0 cm,
Height = ?
Now, we can rearrange the formula to solve for the height:
Height = (2 × Area) / (Side1 + Side2).
Substituting the given values:
Height = (2 × 10.5 cm²) / (5.0 cm + 2.0 cm).
Height = (21 cm²) / (7 cm).
Height = 3 cm.
Therefore, the height of the trapezoid is 3 cm.