Question

HELP ME 7th grade math
What is the total surface area?​

Answer 1

Explanation:

To calculate the total surface area, you first need to calculate the surface area of one of the 4 triangles and multiply that by 4.

We can solve this two ways (I would recommend using 2).

1)

Using herons formula:

a, b, c = different sides of the triangle (length)

s = (a + b + c) / 2

a =
`√(s(s-a)(s-b)(s-c))`

If we input values:

a = b = c = 6.5m

s = (3 * 6.5) / 2 = 9.75

`\sqrt{s(s-6.5)^(3) }` which is about 18.29478 (exact answer:
`3.25√(31.6875)`)

18.29478 * 4 = the entire area = 73.17912 m^2

exact whole area:
`(13√(31.6875))m^(2)`

2)

Each of the four triangles can be divided into 2 more triangles.

(2 * 4 = 8 = total amount of new small triangles)

How we calculate the area of one of the new small ones:

(h * w) / 2 = a

h = 5.6m

w = (width of one of the four triangles width divided by 2) = 3.25m

3.25m * 5.6m = 18.2m^2

18.2m^2 / 2 = 9.1m^2

There are 8 of the new small triangles in the biggest triangle made up of four smaller ones.

So if we take 9.1m^2 * 8, we get the total area!

Total area: 72.8m^2

Happy to help you!

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