Question

Find the surface area of the composite solid. PLZ HELP

Answer 1

`\Huge \boxed{\mathrm{613.5 \ m^2 }}`

`\rule[225]{225}{2}`

Explanation:

We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.

Surface area of the triangular prism:

10 × 8.7 × 1/2 + 16 × 10 × 3

⇒ 523.5

Surface area of the triangular pyramid:

6 × 10 × 1/2 × 3

⇒ 90

Adding the surface areas:

523.5 + 90

⇒ 613.5

`\rule[225]{225}{2}`

Answer 2

Explanation:

Ok, so the surface area is found by adding up all the areas of each individual shape of the entire solid.

I attached a picture of some of the missing values. That should help a little with visualizing.

Since the three rectangles are all the same values, you can substitute adding them by just multiplying lw (their individual areas) by 3.

The three triangles at the top are all the same as well, so you can multiply their areas (
`(1)/(2) bh` ) by 3, too.

Then there's the triangle at the bottom that is by itself, that will just have a 1 in front of it.

Now you can make your surface area equation:

`SA=3lw+3((1)/(2) b_1h_1)+(1)/(2) b_2h_2`

The b1h1 are the three triangles at the top and the b2h2 is the triangle at the bottom.

`SA=3(10)(16)+3((1)/(2))( 10)(6)+(1)/(2) (10)(8.7)\\SA=480+90+43.5\\SA=613.5`

If there's anything you need me to explain further, feel free to comment :)

Answer:

`SA=613.5m^2`