Question

Find the area of the trapezoid-shaped figure given below.

• A. 10 sq units
• B. 12 sq units
• C. 16 sq units
• D. 14 sq units

Answer 1

The correct option is B 12 sq units

Area of the trapezoid ABCDEF = area of the $\Delta ABF$ + area of the square BCEF + area of the $\Delta CDE$
Area of the $\Delta ABF=\frac{1}{2}\times$ base $\times$ height
$=\frac{1}{2}\times AB\times BF$
$=\frac{1}{2}\times 2\times 2$
= 2 sq units

Area of the square BCEF = side $\times$ side
$=BC\times CE$
$=2\times 2=4\text{sq units}$

Area of the $\Delta CDE=\frac{1}{2}\times$ base $\times$ height
$=\frac{1}{2}\times CD\times CE$
$=\frac{1}{2}\times 2\times 6$
= 6 sq units

Area of the trapezoid ABCDEF = 2 + 4 + 6 = 12 sq units

Alternatively, Area of the trapezoid $ABCDEF=\frac{1}{2}\times$ (sum of parallel sides)$\times$ height

Length of first parallel side, EF = 2 units
Length of second parallel side, AD = AB + BC + CD = 2 + 2 + 6 = 10 units
Area of the trapezoid $=\frac{1}{2}\times (EF+AD)\times BF$
$=\frac{1}{2}\times (2+10)\times 2=12\text{sq units}$
Option A is correct.