Find the area of the trapezoid by composition of rectangle and triangles.
A)48
B)72
C)84
D)88
C) 84
To find the area of the trapezoid, we can divide it into a rectangle and two triangles. The trapezoid can be split like this:
1. The top and bottom sides of the trapezoid form the two parallel sides of a rectangle, with a height equal to the distance between the two parallel sides of the trapezoid.
2. The two non-parallel sides of the trapezoid will form two congruent right triangles when extended down to meet the perpendicular line from the top of the trapezoid to the base.
We can calculate the area of each shape separately and then sum them up to find the total area of the trapezoid:
1. Area of the rectangle = base × height = 6 × 6 = 36
2. Area of one triangle = 1/2 × base × height = 1/2 × 6 × 6 = 18
3. Total area = rectangle area + 2 × triangle area = 36 + 2 × 18 = 36 + 36 = 72
Therefore, the area of the trapezoid is 72. So, the correct answer is B) 72.