Answer:
S.A. = 36 cm²
Step-by-step explanation:
First step:
Calculate the hypotenuse of a right triangle.
Use the Pythagorean theorem:
[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\\\\h=5\ cm[/tex]
Second step:
We have
two right triangles with legs a = 3cm and b = 4 cm
one rectangle 4cm × 2cm
one rectangle 3cm × 2cm
one rectangle 5cm × 2cm
Calculate each area:
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
Substitute:
[tex]A_1=\dfrac{(3)(4)}{2}=(3)(2)=6\ cm^2[/tex]
The formula of an area of a rectangle l × w:
[tex]A=lw[/tex]
Substitute:
[tex]A_2=(4)(2)=8\ cm^2\\\\A_3=(3)(2)=6\ cm^2\\\\A_4=(5)(2)=10\ cm^2[/tex]
Third step:
Calculate the Surface Area of the figure:
[tex]S.A.=2A_1+A_2+A_3+A_4[/tex]
Substitute:
[tex]S.A.=2(6)+8+6+10=36\ cm^2[/tex]
