Question

PLEASE HELP FAST! ASAP

Answer 1

S.A = (52 + 120+ 32 + 72 + 12 ) cm ²

Calculate it..

Hope it helps!!

Answer 2

`372cm^(2)`

Explanation:

For this problem, let's find the surface area of each body and then add them.

1. Surface area of the rectangular prism (red color body):

Formula:
`SA=2(wl+hl+hw)`; where w is width, w is height, and l is length.

a) Annotate the values.

l= 12

h= 3

w= 4

b) Substitute in the formula and calculate.

`SA=2((4)(12)+(3)(12)+(3)(4))=2(48+36+12)=192cm^(2)`

2. Surface area of the triangular prism (blue color body):

For this one we are gonna work part by part.

a) Let's calculate the area of the 2 triangular sides first.

Area of a triangle:
`A=(b*h)/(2)`; where b is base and h is height is the triangle.

`A=2(((5)(12))/(2))=2((60)/(2)) =60cm^(2)`

Note: we mltiply by 2 because there are 2 sides with this shape in the body.

b) Area of the back side that touches the rectangular prism.

This part is just a rectangle, hence, it's area formula is:

`A=b*h=(12)(4)=48cm^(2)`

c. Area of the plane that forms a slope.

Is basically another rectangle, hence:

`A=b*h=(13)(4)=52cm^(2)`

d. Area of the part next to the text "5 cm":

Is basically another rectangle, hence:

`A=b*h=(4)(5)=20cm^(2)`

e. Now, the total surface area of this rectangular prism should be the addition of all it's partial areas:

`60+48+52+20=180cm^(2)`

3. Surface area of the composite figure:

`192cm^(2) +180cm^(2) =372cm^(2)`