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 4.5 Triangle Just as the area of parallelogram was derived from the area of rectangle, the area of a triangle can be derived from the area of a parallelogram. Consider the triangle PQR (figure 4.4). If a line is drawn through P parallel to RQ and another line is drawn through Q parallel to PR they will intersect at O. POQR is a parallelogram with PQ as its diagonal. Figure 4.4 Recall that the diagonal of a parallelogram divides the parallelogram into two congruent triangles. \ Area of parallelogram POQR = 2 ´ Area D PQR or Area D PQR = Area of parallelogram POQR. Area of parallelogram POQR = bh where h is the altitude on the base with length h. \ Area D PQR = bh Area of a triangle is half the product of one base and the corresponding altitude. The perimeter of the triangle is simply the sum of all its sides. P = ( a + b + c ) in figure 4.4. Index 4.1 Perimeter 4.2 Square 4.3 Rectangle 4.4 Parallelogram 4.5 Triangle 4.6 Trapezoids 4.7 Circles Chapter 5
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