Question

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

Answer 1

Answer:

Step-by-step 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 = $\sqrt{s(s-a)(s-b)(s-c)}$

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: $3.25\sqrt{31.6875}$)

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

exact whole area: $(13\sqrt{31.6875})m^{2}$

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

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