Question

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

Answer 1

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 $\frac{b_{1} +b_{2} }{2}h$

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