Question

1. find the perimeter and area of the given trapezoid.

Explanation:

Step1: Determine side - lengths

Count the grid - squares for horizontal and vertical sides. For non - vertical/horizontal sides, use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's assume the trapezoid has vertices with coordinates that we can read from the grid. Suppose the parallel sides are $a$ and $b$ and the non - parallel sides are $c$ and $d$. By counting grid squares, if the top base $a = 6$, the bottom base $b= 2$, and for the non - parallel sides, using the distance formula (or Pythagorean theorem for right - angled triangles formed by grid squares). If one non - parallel side has a right - triangle with legs of length 3 and 4, its length $c=\sqrt{3^2 + 4^2}=5$ (similarly for the other non - parallel side $d = 5$).

Step2: Calculate the perimeter $P$

The perimeter of a trapezoid is $P=a + b + c + d$. Substituting the values: $P=6 + 2+5 + 5=18$.

Step3: Calculate the area $A$

The area of a trapezoid is given by the formula $A=\frac{(a + b)h}{2}$, where $h$ is the height. By counting grid squares, the height $h = 3$. Substituting $a = 6$, $b = 2$ and $h = 3$ into the formula: $A=\frac{(6 + 2)\times3}{2}=\frac{8\times3}{2}=12$.

Answer:

Perimeter: 18, Area: 12