Find the area of the trapezoid by decomposing it into other shapes. The numbers are six centimeters five centimeters and eight centimeters what is the other side
To find the area of the trapezoid, we need to know the lengths of both bases. In this case, you have mentioned three sides - six centimeters, five centimeters, and eight centimeters. However, the trapezoid has two parallel sides, so we need to identify which two sides are parallel.
Assuming that the sides of length five centimeters and eight centimeters are the parallel sides, we can proceed with decomposing the trapezoid into other shapes in order to calculate its area.
Let's label the bases of the trapezoid as follows:
Base 1 (parallel to side of length 5 cm) = 5 cm
Base 2 (parallel to side of length 8 cm) = 8 cm
Height (perpendicular distance between the bases) = unknown
Since the trapezoid is decomposed into other shapes, let's consider two right-angled triangles by drawing a vertical line from each vertex of the trapezoid to the base.
|
x/|\
/ | \
/___|___\
6 cm
First, let's calculate the height of the trapezoid by using the Pythagorean theorem.
Using the right triangle on one side:
Height^2 + (Base 1)^2 = (Side)^2
Height^2 + 5^2 = 6^2
Height^2 + 25 = 36
Height^2 = 36 - 25
Height^2 = 11
Taking the square root of both sides:
Height = √11 cm (approximated to two decimal places)
Now, we have all the information needed to calculate the area of the trapezoid.
Area of the trapezoid = (Base 1 + Base 2) * Height / 2
Area = (5 cm + 8 cm) * √11 cm / 2
Area = 13 cm * √11 cm / 2
Area ≈ 28.67 cm^2 (approximated to two decimal places)
Therefore, the area of the trapezoid is approximately 28.67 square centimeters.