Trapezoids
1. One pair of parallel sides
A trapezoid is a quadrilateral with two parallel sides (bases) of different lengths. The other two sides are called legs.
Properties of Trapezoids:
1. Two parallel sides: Trapezoids have two parallel sides (bases) and two non-parallel sides (legs).
2. Base angles: The base angles of a trapezoid are the angles formed by one base and each leg.
3. Adjacent angles: The legs of a trapezoid form two adjacent angles with each base.
4. Median: The median of a trapezoid is the line segment that joins the midpoints of the two non-parallel sides. It is parallel to the bases and half the sum of the bases.
5. Height: The height of a trapezoid is the perpendicular distance between the two parallel bases.
6. Area: The area of a trapezoid is given by the formula A = 1/2(base1 + base2) x height.
7. Perimeter: The perimeter of a trapezoid is the sum of the lengths of all four sides.
Example:
Find the area and perimeter of a trapezoid whose bases are 5 cm and 7 cm, and whose height is 8 cm.
Solution:
We can use the formula: A = 1/2(base1 + base2) x height.
Here, base1 = 5 cm, base2 = 7 cm, and height = 8 cm.
A = 1/2(5 + 7) x 8
A = 1/2(12) x 8
A = 6 x 8
A = 48 cm²
Therefore, the area of the trapezoid is 48 cm².
To find the perimeter, we add the lengths of all four sides:
Perimeter = base1 + base2 + leg1 + leg2
Perimeter = 5 + 7 + (leg1) + (leg2)
Since the legs are not given, we cannot find the exact perimeter.
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