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otez555 [7]
3 years ago
6

When using the given diagram to determine the area of the pentagon by decomposition, which statements are correct?:

Mathematics
1 answer:
pogonyaev3 years ago
6 0

Answer:

Options (B) and (E)

Step-by-step explanation:

Area of ΔABC = \frac{1}{2}(\text{Base})(\text{Height})

                        = \frac{1}{2}(14)(6)

                        = 42 in²

Area of trapezoid ADEC = \frac{1}{2}(b_1+b_2)h

[Here, b_1 and b_2 are the parallel sides and 'h' is the height of the isosceles trapezoid given]

= \frac{1}{2}(10+14)(8)

= 96 in²

Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC

                                    = 42 + 96

                                    = 138 in²

Therefore, Options (B) and (E) are the correct options.

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