Question

The figure is symmetric about the x- and y-axis. what is the area of the figure below

Answer 1

126 units²

Explanation:

Draw 5 vertical lines BR, CQ, EO, GM, HL and we will have 4 trapezoids and 2 rectangles.

Trapezoid ABRS ≅ trapezoid IHLK

Trapezoid DEOP ≅ trapezoid FEON

Rectangle BCQR ≅ rectangle GHLM

Area of trapezoid is
`(b_(1) +b_(2) )/(2)h`

Area of rectangle is
`lw`

The total area of the figure is: ( 2 ×
`A_(ABRS)` + 2 ×
`A_(BCQR)` + 2 ×
`A_(DEOP)` )

In trapezoid ABRS:
`b_(1)` = 6,
`b_(2)` = 8 and h = 3 ⇒

2 ×
`A_(ABRS)` = 2 × [3(6 + 8) ÷ 2] = 42 units²

In rectangle BCQR: l = 6 and w = 3 ⇒

2 ×
`A_(BCQR)` = 2 × (6 × 3) = 36 units²

In trapezoid DEOP:
`b_(1)` = 6,
`b_(2)` = 10 and h = 3 ⇒

2 ×
`A_(DEOP)` = 2 × [3(6 + 10) ÷ 2] = 48 units²

`A_(total)` = 42 + 36 + 48 = 126 units²