1. Find the surface area of the rectangular prism with dimensions 20 m, 7 m, and 3.4 m. The formula for the surface area of a rectangular prism is: $$SA = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height. Calculate each product: $$lw = 20 \times 7 = 140$$ $$lh = 20 \times 3.4 = 68$$ $$wh = 7 \times 3.4 = 23.8$$ Sum these: $$140 + 68 + 23.8 = 231.8$$ Multiply by 2: $$SA = 2 \times 231.8 = 463.6$$ So, the surface area is $463.6$ square meters. 2. Find the surface area of the triangular prism with base edges 7 cm, 4 cm, 12 cm, and height 6 cm. The surface area formula for a triangular prism is: $$SA = bh + (P \times l)$$ where $b$ is the base of the triangle, $h$ is the height of the triangle, $P$ is the perimeter of the triangular base, and $l$ is the length of the prism. Calculate the area of the triangular base: $$Area_{triangle} = \frac{1}{2} \times base \times height = \frac{1}{2} \times 7 \times 6 = 21$$ Calculate the perimeter of the triangle: $$P = 7 + 4 + 12 = 23$$ Calculate the lateral surface area: $$Lateral = P \times l = 23 \times 6 = 138$$ Total surface area: $$SA = 2 \times Area_{triangle} + Lateral = 2 \times 21 + 138 = 42 + 138 = 180$$ So, the surface area is $180$ square centimeters. 3. Find the surface area of the cylinder with radius 15 in and height 48 in. The surface area formula for a cylinder is: $$SA = 2\pi r^2 + 2\pi rh$$ where $r$ is the radius and $h$ is the height. Calculate the area of the two circular bases: $$2\pi r^2 = 2 \times 3.14 \times 15^2 = 2 \times 3.14 \times 225 = 1413$$ Calculate the lateral surface area: $$2\pi rh = 2 \times 3.14 \times 15 \times 48 = 4521.6$$ Total surface area: $$SA = 1413 + 4521.6 = 5934.6$$ So, the surface area is $5934.6$ square inches.