Answer: 30
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Explanation:
Each tickmark on the graph represents a distance of 2 units. From A to P is 4 tickmarks, so that corresponds to 2*4 = 8 units. That's one of the bases. The other base is TR = 2. The bases are parallel to one another.
The height is always perpendicular to the base, and the height is 2*3 = 6 units.
So we have
b1 = 8, b2 = 2, and h = 6
Which means,
A = h*(b1+b2)/2
A = 6*(8+2)/2
A = 6*10/2
A = 60/2
A = 30
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As a slightly longer alternative, we can plot points at (-2, 0) and (-2, -2). Let's call these two points M and N respectively. These two points subdivide the trapezoid into three pieces: Two triangles sandwiching a rectangle.
- Triangle TMP has area of base*height/2 = 6*4/2 = 12
- Rectangle TMNR has area of length*width = 6*2 = 12
- Triangle RNA has area of base*height/2 = 6*2/2 = 6
Add up those sub-areas to get the full area of the trapezoid:
12+12+6 = 30
