The surface area of a triangle is: s = (base * height)/2
First pyramid:
The surface area of the red triangle is:
s = (base * height)/2 → where: base = 2
s = (2 * height)/2 → where: height = 3
s = (2 * 3)/2
s = 3 in² → the pyramid has 4 triangles, so you multiply by 4
= 4 * 3 in²
= 12 in² → and you add the surface area of the yellow square
= 12 in² + (surface area of the yellow square) → the surface area of the yellow square is: 2 * 2 = 4 in²
= 12 in² + 4 in²
= 16 in² ← this is the surface area of the first pyramid
Second pyramid:
The surface area of the blue triangle is:
s = (base * height)/2 → where: base = 4
s = (4 * height)/2 → where: height = 4
s = (4 * 4)/2
s = 8 in² → the pyramid has 4 triangles, so you multiply by 4
= 4 * 8 in²
= 32 in² → and you add the surface area of the green square
= 32 in² + (surface area of the green square) → the surface area of the green square is: 4 * 4 = 16 in²
= 32 in² + 16 in²
= 48 in² ← this is the surface area of the second pyramid
Third pyramid:
The surface area of the grey triangle is:
s = (base * height)/2 → where: base = 3
s = (3 * height)/2 → where: height = 6
s = (3 * 6)/2
s = 9 in² → the pyramid has 4 triangles, so you multiply by 4
= 4 * 9 in²
= 36 in² → and you add the surface area of the pink square
= 36 in² + (surface area of the pink square) → the surface area of the pink square is: 3 * 3 = 9 in²
= 36 in² + 9 in²
= 45 in² ← this is the surface area of the third pyramid
The total surface area of the 3 pyramids is:
= 48 + 36 + 45
= 129 in² → as Laura needs one tube for every 30 in², the number of tubes is:
n = 129/30
n = 4.3 tubes → rounded
n = 5 tubes (over the proposal choices)
But if you consider only the triangle, i.e. without the square, the total surface area is:
= 129 - (yellow square) - (green square) - (pink square)
= 129 - 4 - 16 - 9
= 100 in² → as Laura needs one tube for every 30 in², the number of tubes is:
n = 100/30
n = 10/3
n = 3.33 tubes → rounded
n = 4 tubes ← choice A)