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To derive the formula for area of a triangle from the formula for the area of a rectangle, cut out a triangle as in Figure 23(a); fold a perpendicular to the base with measurement b and containing point B to find the height h; and fold the altitude in half, as shown in Figure23(b). Next fold along the colored segments in the trapezoid in Figure23(c) to obtain rectangle in Figure 23(d).
a. What is the area of the rectangle in Figure 23(d)?
b. How can the formula for the area of a triangle be developed from your answer in part (a)?
(a)
To find:
The area of rectangle of Figure 23(d).
Answer to Problem 4NT
Solution:
Area of rectangle be
Explanation of Solution
Given:
A rectangle with dimension
Approach:
Calculation:
(b)
To find:
The area of triangle from rectangle of figure 23(d).
Answer to Problem 4NT
Solution:
Explanation of Solution
Given:
A rectangle of dimension
Approach:
Calculation:
Here rectangle, Figure
So,
Thus
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