Question

Find the area and perimeter of fig ABCD where B=90 and angle DAC=90 degrees. AB=6cm and BC=8cm and DA=24cm

Answer 1

Answer:

$96\ \text{cm}^2$

$17.1\ \text{cm}$

Step-by-step explanation:

$DC$ is the length of the hypotenuse of the triangle $CED$.

So

$DC=\sqrt{ED^2+EC^2}\\\Rightarrow DC=\sqrt{16^2+6^2}\\\Rightarrow DC=17.1\ \text{cm}$

The perimeter of the $ABCD$ is $17.1\ \text{cm}$

$AB+AD+DC+CB=6+24+17.1+8=55.1\ \text{cm}$

The Area of $ABCD$ would be

Area of rectangle ABEC+Area of triangle CED

$8\times 6+\dfrac{1}{2}\times 16\times 6=96\ \text{cm}^2$

The area of the figure $ABCD$ is $96\ \text{cm}^2$.