Question

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

Answer choices:
(A) Area of ∆ABC = 84 in²
(B) Area of ∆ABC = 42 in²
(C) Area of trapezoid = 1/2(14 ÷ 10)8
(D) The area of the pentagon is 180 in²
(E) The area of the pentagon is 138 in²
APPLY TO ALL THAT IS TRUE

Answer 1

The true statements includes

(B) Area of ∆ABC = 42 in²

(E) The area of the pentagon is 138 in²

How to find the true statement

The area of the triangle ABC is solved by the formula

= 1/2 base * height

= 1/2 * 14 * 6

= 42 in²

Area of the trapezoid is solved using the formula

= 1/2 (sum of parallel lines) * height

= 1/2 (14 + 10) 8

= 1/2 (24) * 8

= 96 in²

The area of the pentagon

= 96 + 42

= 138 in²

Answer 2

Options (B) and (E)

Explanation:

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

=
`(1)/(2)(14)(6)`

= 42 in²

Area of trapezoid ADEC =
`(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]

=
`(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.