Question

Find the area of the following figure.
​

Answer 1

${}$

GIVEN THAT,

• AB=9cm
• AF=4.5cm
• EC=13cm
• DG=6.5cm

${}$

To find:- Area of ABCDE

Answer =91.75cm

${}$

$\tt{\green{Step\ By\ Step\ Explaination:-}}$

Now In trapezium ABCE, we have

• sum of parallel sides= AB+EC= 9+14cm
• Height= AF= 4.5cm

${}$

$\tt{→Area\ of\ trapezium\ ABCE= \dfrac{1}{2} \times (sum\ of\ parallel\ sides) \times Height}$

$\tt{→Area\ of\ trapezium\ ABCE= \dfrac{1}{2} \times (9+13) \times 4.5}$

$\tt{→Area\ of\ trapezium\ ABCE= \dfrac{1}{\cancel{2}} \times (\cancel{22} ¹¹) \times 4.5}$

$\tt{→Area\ of\ trapezium\ ABCE= 11 \times 4.5}$

$\tt{→Area\ of\ trapezium\ ABCE= 49.5cm²}$

Now in ∆CDE, we have

• BASE= EC=13cm
• HEIGHT=DG=6.5cm

${}$

Area of triangle =We have

$\sf{→area\ of\ triangle\ CDE = \dfrac{1}{2} \times base \times height}$

$\sf{→area\ of\ triangle\ CDE= \dfrac{1}{2} \times 13 \times 6.5}$

$\sf{→area\ of\ triangle\ CDE= 6.5 \times 6.5}$

$\sf{→area\ of\ triangle\ CDE= 42.25cm²}$

${}$

$\sf\red{area\ of\ figure\ ABCDE\ =}\green{area\ of\ trapezium\ ABCE}+ \pink{area\ of\ triangle\ CDE}$

$\sf\red{area\ of\ figure\ ABCDE\ =}\green{49.5}+ \pink{42.25}$

$\sf \red{area\ of\ figure\ ABCDE\ = \pink{91.75cm²}}$

${}$