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A parallelogram is shown below:

A parallelogram ABCD is shown with DC equal to 9 feet and the perpendicular distance between AB and DC equal to 8 over 9 foot.

Part A: What is the area of the parallelogram? Show your work. (5 points)

Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)

A Parallelogram Is Shown Below A Parallelogram ABCD Is Shown With DC Equal To 9 Feet And The Perpendicular Distance Between AB And DC Equal To 8 Over 9 Foot Par class=

Sagot :

Answer:

a). Area of the parallelogram = 8 cm²

b). Area of both the triangles = 4 cm²

Step-by-step explanation:

a). Area of the given parallelogram ABCD = Base × Height

                                                                 = DC × (Vertical distance between

                                                                              AB and DC)

                                                                 = 9 × [tex]\frac{8}{9}[/tex]

                                                                 = 8 ft²

b). If we decompose this parallelogram into two triangles ΔABC and ADC by a diagonal AC,

Area of both the triangles will be equal.

(Since, diagonal of a parallelogram divides the parallelogram into two equal triangles)

Therefore, area of ΔABC = Area of ΔADC = 4 ft²

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