Question

volume
figure
surface area
$ell=18$ ft
$ell=15$ in
$h=10.4$ ft

Explanation:

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First Pyramid (Square Base, $\ell=18$ ft, $h=16$ ft, base side=7 ft)

Step1: Calculate base area

Base is square: $B = s^2 = 7^2 = 49$ ft²

Step2: Calculate Volume

Volume formula: $V=\frac{1}{3}Bh$
$V=\frac{1}{3} \times 49 \times 16 = \frac{784}{3} \approx 261.33$ ft³

Step3: Calculate lateral surface area

Each triangular face area: $\frac{1}{2} \times s \times \ell = \frac{1}{2} \times 7 \times 18 = 63$ ft²
4 faces: $4 \times 63 = 252$ ft²

Step4: Calculate total surface area

Total SA = Lateral SA + Base Area
$SA = 252 + 49 = 301$ ft²

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Second Pyramid (Rectangular Base, $\ell=15$ in, $h=7.2$ in, base sides=13 in, 18 in)

Step1: Calculate base area

Base is rectangle: $B = 13 \times 18 = 234$ in²

Step2: Calculate Volume

$V=\frac{1}{3}Bh = \frac{1}{3} \times 234 \times 7.2 = 78 \times 7.2 = 561.6$ in³

Step3: Calculate lateral surface area

Two pairs of triangular faces:
First pair (13 in base): $2 \times (\frac{1}{2} \times 13 \times 15) = 195$ in²
Second pair (18 in base): $2 \times (\frac{1}{2} \times 18 \times 15) = 270$ in²
Total Lateral SA = $195 + 270 = 465$ in²

Step4: Calculate total surface area

Total SA = $465 + 234 = 699$ in²

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Third Pyramid (Square Base, $h=10.4$ ft, slant height=12.8 ft, base side=9 ft)

Step1: Calculate base area

$B = 9^2 = 81$ ft²

Step2: Calculate Volume

$V=\frac{1}{3}Bh = \frac{1}{3} \times 81 \times 10.4 = 27 \times 10.4 = 280.8$ ft³

Step3: Calculate lateral surface area

Each triangular face area: $\frac{1}{2} \times 9 \times 12.8 = 57.6$ ft²
4 faces: $4 \times 57.6 = 230.4$ ft²

Step4: Calculate total surface area

Total SA = $230.4 + 81 = 311.4$ ft²

Answer:

Volume	Surface Area
561.6 in³	699 in²
280.8 ft³	311.4 ft²