Respuesta :

gmany

Answer:

[tex]\large\boxed{S.A.=116\ cm^2}[/tex]

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

[tex]x^2+3^2=5^2[/tex]

[tex]x^2+9=25[/tex]                 subtract 9 from both sides

[tex]x^2=16\to x=\sqrt{16}\\\\x=4[/tex]

The Surface Area:

we have two congruent right triangles and three rectangles

The area of a right triangle:

[tex]A_T=\dfrac{(3)(4)}{2}=6\ cm^2[/tex]

The areas of the rectangles:

[tex]A_{R1}=(5)(7)=35\ cm^2\\\\A_{R2}=(3)(7)=21\ cm^2\\\\A_{R3}=(4)(7)=28\ cm^2[/tex]

The Surface Area:

[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot6+35+21+48=116\ cm^2[/tex]

Ver imagen gmany
imlittlestar

Answer:

Surface area = 96 cm²

Step-by-step explanation:

From the figure we can see that, a prism

To find the height of triangles

Height²= Hypotenuse² - Base 2 = 5² - 3² = 16

Height = 4

To find the surface area

Surface area = Area of two triangles + Area of 2 side face + Area of base

Area of triangles

Area = bh/2 = (3 * 4)/2 = 6 cm²

Area of 2 triangles = 2 * 6 = 12 cm²

Area of side face

Area first face = 7 * 3 = 21 cm ²

Area of second face  = 7 * 4 = 28 cm ²

Total area of side face = 21 + 28 = 49 cm²

Area of base

Area of base = 7 * 5 = 35 cm²

Total surface area = 12 + 49 + 35  = 96 cm²

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