Question

example: surface area = base area + \\(\frac{1}{2}\\) × perimeter × slant height base area = side × side = 6 × 6 = 36 yd² perimeter = 4 × side = 4 × 6 = 24 yd surface area = 36 + \\(\frac{1}{2}\\) × 24 × 10 = 156 yd² find the surface area of each square pyramid. 1) surface area = ____ 2) surface area = __ 3) surface area = __ 4) surface area = __ 5) surface area = __ 6) surface area = ____

Explanation:

Step1: Calculate base area

$A_{base} = s^2$

Step2: Calculate base perimeter

$P = 4s$

Step3: Calculate surface area

$SA = A_{base} + \frac{1}{2} \times P \times l$
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For Pyramid 1 (8 ft base, 16 ft slant height):

Step1: Compute base area

$A_{base} = 8^2 = 64$ ft²

Step2: Compute base perimeter

$P = 4 \times 8 = 32$ ft

Step3: Compute total surface area

$SA = 64 + \frac{1}{2} \times 32 \times 16 = 64 + 256 = 320$ ft²

For Pyramid 2 (4 yd base, 10 yd slant height):

Step1: Compute base area

$A_{base} = 4^2 = 16$ yd²

Step2: Compute base perimeter

$P = 4 \times 4 = 16$ yd

Step3: Compute total surface area

$SA = 16 + \frac{1}{2} \times 16 \times 10 = 16 + 80 = 96$ yd²

For Pyramid 3 (11 in base, 16 in slant height):

Step1: Compute base area

$A_{base} = 11^2 = 121$ in²

Step2: Compute base perimeter

$P = 4 \times 11 = 44$ in

Step3: Compute total surface area

$SA = 121 + \frac{1}{2} \times 44 \times 16 = 121 + 352 = 473$ in²

For Pyramid 4 (3 in base, 11 in slant height):

Step1: Compute base area

$A_{base} = 3^2 = 9$ in²

Step2: Compute base perimeter

$P = 4 \times 3 = 12$ in

Step3: Compute total surface area

$SA = 9 + \frac{1}{2} \times 12 \times 11 = 9 + 66 = 75$ in²

For Pyramid 5 (6 ft base, 12 ft slant height):

Step1: Compute base area

$A_{base} = 6^2 = 36$ ft²

Step2: Compute base perimeter

$P = 4 \times 6 = 24$ ft

Step3: Compute total surface area

$SA = 36 + \frac{1}{2} \times 24 \times 12 = 36 + 144 = 180$ ft²

For Pyramid 6 (9 yd base, 14 yd slant height):

Step1: Compute base area

$A_{base} = 9^2 = 81$ yd²

Step2: Compute base perimeter

$P = 4 \times 9 = 36$ yd

Step3: Compute total surface area

$SA = 81 + \frac{1}{2} \times 36 \times 14 = 81 + 252 = 333$ yd²

Answer:

1. $320$ ft²
2. $96$ yd²
3. $473$ in²
4. $75$ in²
5. $180$ ft²
6. $333$ yd²