Question

Find the area of pentagon ABCDE, given that EB = 10 cm, DC = 5 cm, AF = 3 cm and DG = 4 cm.

• A. 15 $c{m}^2$
• B. 30 $c{m}^2$
• C. 45 $c{m}^2$
• D. 60 $c{m}^2$

Answer 1

The correct option is C 45 $c{m}^2$

Given,
EB = 10 cm,
DC = 5 cm
AF = 3 cm and
DG = 4 cm.

Area of pentagon ABCDE
= Area of trapezium BCDE + Area of $△$AEB

Area of trapezium BCDE
$=\frac{1}{2}\times \left(Sumofparallelsides\right)\times height$
$=\frac{1}{2}\times (CD+BE)\times DG$
$=\frac{1}{2}\times (5+10)\times 4$
$=\frac{1}{2}\times \left(15\right)\times 4$
= 15$\times$2
= 30 $c{m}^2$

Area of $△$AEB
$=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times BE\times AF$
$=\frac{1}{2}\times 10\times 3=15c{m}^2$

Area of pentagon ABCDE
= Area of trapezium BCDE + Area of $△$AEB
= 30 $c{m}^2$ + 15 $c{m}^2$
= 45 $c{m}^2$