Question

In the figure $ABCD$ and $BEFG$ are two squares with side lengths 4 cm and 10 cm respectively. Find the area of the shaded region (sq. cm).

Answer 1

Given: $AB=4cm$

$BE=10cm$

$F(14,10)$

$A(0,0)$

Let $A$ be the origin then equation of line $AF$

$y=mxm=\frac{y_2-y_1}{x_2-x_1}=\frac{14-0}{10-0}$

$y=\frac{7}{5}x$

for $x=4cmy=\frac{28}{5}cm$ which are co-ordinates of $P.$

$P(4,\frac{28}{5})$

Area of $△APB$

$\Rightarrow$ $\frac{1}{2}\times base\times height=\frac{1}{2}\times AB\times BP$

$=\frac{1}{2}\times A\times \frac{28}{5}$

$=11.2c{m}^2$.