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). 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 ×

                                                                 = 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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