Given PSTQ is a trapezoid, ST = 4, PQ = 25, PS = 13, TQ = 20
Find: Area of PSTQ
To find the area of trapezoid PSTQ, we can use the formula for the area of a trapezoid:
Area = (1/2) * (b1 + b2) * h
where b1 and b2 are the lengths of the two parallel bases and h is the height of the trapezoid.
In this case, the lengths of the parallel bases are PQ = 25 and ST = 4, and the height of the trapezoid can be found by drawing an altitude from P to line TQ, forming a right triangle.
Using Pythagorean theorem in the right triangle PST, we can find the height:
PS^2 = PT^2 + TS^2
13^2 = h^2 + 20^2
169 = h^2 + 400
h^2 = 231
h ≈ √231 ≈ 15.2
Now we can plug in the values into the formula:
Area = (1/2) * (25 + 4) * 15.2
Area = (1/2) * 29 * 15.2
Area = 217.6
Therefore, the area of trapezoid PSTQ is 217.6 square units.