To describe: How to formula for the area of the trapezoid is related to the formula of area of a
Answer to Problem 39HP
Area of trapezoid is the sum of total area of three triangles forming inside it, having same heights as of trapezoid.
Explanation of Solution
Given information: Formula of area of a trapezoid and the formula of area of the triangle.
Formula/Concept used:
Area of a trapezoid
And Area of a triangle
Now to show that area of trapezoid is actually the sum of areas of three triangles, forming inside it.
Calculation: Let ABCD be the trapezoid, divided into three triangles ADH, AHB and BHC, with having same heights h , as shown below :
Area of a triangle ADH
Area of a triangle AHB
Area of a triangle BHC
On adding all above areas
Area of a triangle ADH+ Area of a triangle AHB+ Area of a triangle BHC
= Area of trapezoid ABCD
Conclusion: By above calculation, it is cleared, that area of the trapezoid is actually the sum of areas of three triangle forming inside it, having same heights as of trapezoid.
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