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

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Boffeemadrididn

Answer:

[tex]96\ \text{cm}^2[/tex]

[tex]17.1\ \text{cm}[/tex]

Step-by-step explanation:

[tex]DC[/tex] is the length of the hypotenuse of the triangle [tex]CED[/tex].

So

[tex]DC=\sqrt{ED^2+EC^2}\\\Rightarrow DC=\sqrt{16^2+6^2}\\\Rightarrow DC=17.1\ \text{cm}[/tex]

The perimeter of the [tex]ABCD[/tex] is [tex]17.1\ \text{cm}[/tex]

[tex]AB+AD+DC+CB=6+24+17.1+8=55.1\ \text{cm}[/tex]

The Area of [tex]ABCD[/tex] would be

Area of rectangle ABEC+Area of triangle CED

[tex]8\times 6+\dfrac{1}{2}\times 16\times 6=96\ \text{cm}^2[/tex]

The area of the figure [tex]ABCD[/tex] is [tex]96\ \text{cm}^2[/tex].

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