Question

find the perimeter and area of the figure below.
155
146
123
143
306
perimeter =
area =

Explanation:

Step1: Calculate the perimeter

The perimeter of a trapezoid is the sum of all its side lengths.
So, we add the lengths \(155\), \(143\), \(306\), and \(146\).
\(Perimeter = 155 + 143 + 306 + 146\)
First, add \(155 + 143 = 298\), then \(298 + 306 = 604\), and finally \(604 + 146 = 750\).

Step2: Calculate the area

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the two parallel sides (the bases), and \(h\) is the height.
Here, \(a = 155\), \(b = 306\), and \(h = 123\).
So, \(A=\frac{(155 + 306)\times123}{2}\)
First, calculate the sum of the bases: \(155+306 = 461\).
Then, multiply by the height: \(461\times123 = 56703\).
Finally, divide by 2: \(\frac{56703}{2}=28351.5\).

Answer:

Perimeter = \(\boldsymbol{750}\)
Area = \(\boldsymbol{28351.5}\)