Answer:
126 units²
Step-by-step 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 [tex]\frac{b_{1} +b_{2} }{2}h[/tex]
Area of rectangle is [tex]lw[/tex]
The total area of the figure is: ( 2 × [tex]A_{ABRS}[/tex] + 2 × [tex]A_{BCQR}[/tex] + 2 × [tex]A_{DEOP}[/tex] )
In trapezoid ABRS: [tex]b_{1}[/tex] = 6, [tex]b_{2}[/tex] = 8 and h = 3 ⇒
2 × [tex]A_{ABRS}[/tex] = 2 × [3(6 + 8) ÷ 2] = 42 units²
In rectangle BCQR: l = 6 and w = 3 ⇒
2 × [tex]A_{BCQR}[/tex] = 2 × (6 × 3) = 36 units²
In trapezoid DEOP: [tex]b_{1}[/tex] = 6, [tex]b_{2}[/tex] = 10 and h = 3 ⇒
2 × [tex]A_{DEOP}[/tex] = 2 × [3(6 + 10) ÷ 2] = 48 units²
[tex]A_{total}[/tex] = 42 + 36 + 48 = 126 units²
