This problem asks for the area of a trapezoid in square inches. The formula for area of a trapezoid is A = ½ × (base₁ + base₂) × height. Substituting the given values: A = ½ × (10 + 16) × 7 = ½ × 26 × 7 = 91 in². A common error is forgetting to divide by 2, which would give 182 in². When working with trapezoids, remember to add both bases before multiplying by height and dividing by 2.

This problem asks for the area of a circular garden given its diameter in square meters. The formula for area of a circle is A = πr², where r is the radius. Since diameter = 14 m, the radius = 14 ÷ 2 = 7 m. Substituting: A = 3.14 × (7)² = 3.14 × 49 = 153.86 m². A common error is using diameter instead of radius in the formula, which would give A = 3.14 × (14)² = 615.44 m². Always convert diameter to radius before using the area formula.

This problem asks for the volume of a rectangular prism in cubic inches. The formula for volume of a rectangular prism is V = length × width × height. Substituting the given values: V = 8 × 5 × 3 = 120 in³. A common error is adding the dimensions (8 + 5 + 3 = 16) or multiplying only two dimensions (8 × 5 = 40). Always remember that volume requires multiplying all three dimensions together.

This problem asks for the area of a right triangle given the lengths of its legs in square centimeters. For a right triangle, the area formula is A = ½ × leg₁ × leg₂. Substituting the given values: A = ½ × 9 × 12 = ½ × 108 = 54 cm². A common error is forgetting to multiply by ½, which would give 108 cm². Remember that for right triangles, the two legs serve as the base and height, making the calculation straightforward.

This problem asks for the area of a triangle given coordinates of its vertices in square units. Since the triangle has a horizontal base from A(1,1) to B(7,1), the base length is 7 - 1 = 6 units. The height is the vertical distance from this base to C(1,5), which is 5 - 1 = 4 units. Using the formula Area = ½ × base × height: Area = ½ × 6 × 4 = 12 square units. A common error is forgetting to multiply by ½, which would give 24 square units. When working with coordinate geometry, sketch the triangle to visualize the base and height.

This problem asks for the volume of a cylindrical water tank in cubic feet. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Substituting the given values: V = 3.14 × (3)² × 10 = 3.14 × 9 × 10 = 282.6 ft³. A common error is using diameter instead of radius, which would give 3.14 × (6)² × 10 = 1130.4 ft³. When working with cylinders, always verify whether you're given radius or diameter before calculating.

This problem asks for the height of a cylinder given its volume and radius in centimeters. The volume formula V = πr²h can be rearranged to h = V/(πr²). Substituting: h = 500/(3.14 × 5²) = 500/(3.14 × 25) = 500/78.5 = 6.369..., which rounds to 6.4 cm. A common error is forgetting to square the radius, which would give h = 500/(3.14 × 5) = 31.8 cm. When solving for a missing dimension, carefully rearrange the formula before substituting values.

This problem asks for the volume of a square pyramid in cubic inches. The formula for volume of a pyramid is V = (1/3) × base area × height. The base is a square with side 10 in, so base area = 10² = 100 in². Volume = (1/3) × 100 × 12 = (1/3) × 1200 = 400 in³. A common error is forgetting to divide by 3, which would give 1200 in³. Remember that pyramid volume is always one-third of the prism volume with the same base and height.

This problem asks for the area of a rectangle given its vertices in square units. The rectangle has width from x = -2 to x = 4, which is 4 - (-2) = 6 units. The height is from y = 1 to y = 6, which is 6 - 1 = 5 units. Area = width × height = 6 × 5 = 30 square units. A common error is miscalculating the distances when dealing with negative coordinates; remember to subtract the smaller coordinate from the larger.

This problem asks for the area of a parallelogram in square feet. The formula for area of a parallelogram is A = base × height. Substituting the given values: A = 13 × 7 = 91 ft². A common error is using the slant side length instead of the perpendicular height, or trying to use a triangle formula. Remember that for parallelograms, you need the perpendicular height, not the side length.