This problem asks for the total area of a composite figure consisting of a rectangle and a semicircle. The rectangle has area 10 m × 6 m = 60 m², and the semicircle has diameter 6 m (radius 3 m), giving it area ½πr² = ½π(3)² = 9π/2 m². The total area is 60 + 9π/2 m². A common mistake is using the full circle formula πr² instead of halving it for a semicircle, or confusing diameter with radius. When working with composite figures, calculate each component separately before adding.

This problem asks for the total surface area of a right rectangular prism with dimensions 8 in × 5 in × 3 in. The formula for surface area of a rectangular prism is SA = 2(lw + lh + wh), where l, w, and h are length, width, and height. Substituting: SA = 2(8×5 + 8×3 + 5×3) = 2(40 + 24 + 15) = 2(79) = 158 in². A common error is forgetting to multiply by 2 (counting only one face of each pair) or miscounting the number of faces. Remember that a rectangular prism has 6 faces in 3 pairs of congruent rectangles.

This question asks for the volume of a cylindrical water tank in cubic feet. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values: V = π(3²)(10) = π(9)(10) = 90π cubic feet. Using π ≈ 3.14, we get V = 90(3.14) = 282.6 cubic feet. A common error is using diameter instead of radius, which would give 1130.4 cubic feet. When dealing with cylinders, always verify whether you're given radius or diameter.

This question asks for the area of a triangle with vertices in the coordinate plane. For a triangle with vertices at coordinates, we can use the formula: Area = ½|base × height|. The base AB lies along the x-axis from (0,0) to (6,0), so base = 6 units. The height is the perpendicular distance from C(2,5) to the x-axis, which is 5 units. Therefore, Area = ½(6)(5) = 15 square units. A common mistake is using the distance formula unnecessarily or miscalculating the height. For triangles with one side on an axis, identify the base and height directly from coordinates.

This question asks for the area of a trapezoid given its two bases and height. The area of a trapezoid is A = ½h(b₁ + b₂), where h is the height and b₁, b₂ are the parallel bases. Substituting: A = ½(5)(8 + 14) = ½(5)(22) = ½(110) = 55 square meters. A common mistake is forgetting to divide by 2 or adding the bases incorrectly. Remember that the trapezoid formula averages the two bases and multiplies by height.

This question asks for the volume of a right triangular prism. The volume is V = (base area) × length. The triangular base has legs 6 in and 8 in, so its area is ½(6)(8) = 24 square inches. The prism length is 10 inches, so V = 24 × 10 = 240 cubic inches. A common error is forgetting the ½ in the triangle area formula, which would give 480 cubic inches. For prisms, always calculate the base area first, then multiply by the prism's length or height.

This question asks for the area of a right triangle given the lengths of its two legs. The area of a right triangle is A = ½(base)(height), where the legs serve as base and height. Substituting: A = ½(9)(12) = ½(108) = 54 square centimeters. A common error is forgetting the factor of ½ in the triangle area formula, which would give 108 cm². For right triangles, the legs are perpendicular, making them perfect choices for base and height.

This question asks for the area of a composite figure: a rectangle with a triangle removed. The rectangle has area 12 × 9 = 108 square centimeters. The removed right triangle has legs 5 cm and 9 cm, so its area is ½(5)(9) = 22.5 square centimeters. The remaining area is 108 - 22.5 = 85.5 square centimeters. A key insight is recognizing that the triangle shares the rectangle's sides, making calculation straightforward. For composite figures with removed sections, calculate the whole then subtract.

This question asks for the area of a rectangular floor in square yards, given dimensions in feet. First, find the area in square feet: Area = 12 ft × 9 ft = 108 square feet. Since 1 yard = 3 feet, we have 1 square yard = 9 square feet. Converting: 108 ÷ 9 = 12 square yards. A critical error is converting linear feet to yards (dividing by 3) instead of square feet to square yards (dividing by 9). Always square the conversion factor when converting area units.

This question asks for the area of a rectangle given its four vertices in the coordinate plane. The vertices form a rectangle with horizontal sides from x = 1 to x = 7 (length = 6 units) and vertical sides from y = 2 to y = 6 (width = 4 units). Area = length × width = 6 × 4 = 24 square units. A common mistake is miscounting the distance between coordinates by forgetting to subtract. For rectangles with sides parallel to axes, simply find the differences in x and y coordinates.