The coordinates of P is (0,1), Q is (0,3), R is (2,0) and S is (1,0). The area of the trapezoid PQRS is ______ (round off to 1 decimal place). 
To calculate the area of trapezoid PQRS, we'll use the formula for the area of a trapezoid with vertices at coordinates:
P(0,1), Q(0,3), R(2,0), and S(1,0).
The formula for the area of a trapezoid with vertices (x1, y1), (x2, y2), (x3, y3), (x4, y4) is:
Area = 0.5 × |x1y2 + x2y3 + x3y4 + x4y1 - y1x2 - y2x3 - y3x4 - y4x1|
Substituting the given points:
Area = 0.5 × |0×3 + 0×0 + 2×0 + 1×1 - (1×0 + 3×2 + 0×1 + 0×0)|
= 0.5 × |0 + 0 + 0 + 1 - (0 + 6 + 0 + 0)|
= 0.5 × |1 - 6|
= 0.5 × |-5|
= 0.5 × 5
= 2.5
The area of the trapezoid is 2.5, which fits within the given range (2.49, 2.51).
Important Questions from Calculus
- f(x) = 2x2 – 1, then f(0) = _______.
Find the value of integral I = \(\smallint \frac{1}{{x + \sqrt x }}\)dx. (where c = constant)
Differentiate (a cos 3t) w.r.t. to (a sin 3t)
Find the slope of normal to the curve y = x2 + 7x at (1, 8).
Find the equation of normal to the curve y = 4x - 3x2 at (2, -4).
