Question

Need help with finding the area of this prism

Answer 1

`\large\boxed{S.A.=116\ cm^2}`

Explanation:

Look at the picture.

Use the Pythagorean theorem:

`x^2+3^2=5^2`

`x^2+9=25` subtract 9 from both sides

`x^2=16\to x=√(16)\\\\x=4`

The Surface Area:

we have two congruent right triangles and three rectangles

The area of a right triangle:

`A_T=((3)(4))/(2)=6\ cm^2`

The areas of the rectangles:

`A_(R1)=(5)(7)=35\ cm^2\\\\A_(R2)=(3)(7)=21\ cm^2\\\\A_(R3)=(4)(7)=28\ cm^2`

The Surface Area:

`S.A.=2A_T+A_(R1)+A_(R2)+A_(R3)\\\\S.A.=2\cdot6+35+21+48=116\ cm^2`

Answer 2

Surface area = 96 cm²

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