Question

Find the area of the following shape. you must show all work to receive credit

Answer 1

Answer with explanation:

Join AC and FG.Draw BN ⊥ AC.

AC=9 units, BN=3 units, CG=3 units, GF=6 units, FE=4 units,GD=3 Units

Area (ΔABC)

              $=\frac{1}{2} \times {\text{Base}} \times \text{Height}\\\\=\frac{1}{2} \times {BN} \times {AC}\\\\=\frac{1}{2} \times 9 \times 3\\\\=\frac{27}{2}\text{Square units}$  

Area of Trpzoid

            $=\frac{1}{2} \times [\text{Sum of Parallel sides}] \times [\text{Perpendicular Distance between them}]$

Area of Trpzoid ACGF

         $=\frac{1}{2} \times [AC+GF]\times CG\\\\=\frac{1}{2} \times [9+6]\times 3\\\\=\frac{45}{2}\text{Square units}$

Area of Trpzoid FGDE

        $=\frac{1}{2} \times [FE+GD]\times FG\\\\=\frac{1}{2} \times [3+4]\times 6\\\\=21\text{Square units}$

Area of given shape

               $=\frac{27}{2}+\frac{45}{2}+21\\\\=36+21\\\\=57 \text{Square units}$