Question

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

Answer 1

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.