To calculate the area of the shaded region.
Answer to Problem 20PPS
Explanation of Solution
Given information:
The figure consists of a trapezoid along with a non-shaded
Trapezoid has sides
Triangle of
Formula used: Area of trapezoid
Area of triangle
Pythagoras theorem will be used for finding the perpendicular height using
Here ‘p’ is the perpendicular height, ‘b’ is the base and ‘h’ is the hypotenuse of the right-angled triangle.
Calculation:
Calculate the height of the given figure first. This will enable to determine the overall area as well as the area of the non-shaded right-angle triangle present within the figure.
Using Pythagoras theorem.
Since the value of the perpendicular height is needed, arrange the equation with keeping ‘p’ in the left-hand side.
On further simplification
Putting the values in the expression.
After this,
Taking the square root.
Calculation of area of the figure, that is a trapezoid.
Putting the values in the equation.
On further simplification.
Multiplying
Total area
Area of the unshaded triangle.
Formula of area of the triangle.
Putting values in the formula.
Multiply the same.
Area of shaded region
Subtract area of unshaded region from area of complete figure.
Subtracting the same.
Chapter 11 Solutions
Pre-Algebra Student Edition
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