Grade 6 Math Practice Test: Area, Surface Area and Volume

Area of a parallelogram = base × height = 9 × 5 = 45 square centimeters. The height must be perpendicular to the base; 54 uses the slanted 6 cm side instead, and 22.5 takes half as if the shape were a triangle.

Area of a triangle = 12 × base × height = 12 × 8 × 15 = 60 square feet. 120 forgets to take half, and 23 adds the two lengths instead of multiplying.

Area = 12 × (6 + 10) × 4 = 12 × 16 × 4 = 32 square inches. You can also split it into a 6 × 4 rectangle (24) and two triangles that together make 8. 64 forgets to take half.

Think of a full 10 × 8 rectangle (80 square feet) and subtract the missing 4 × 3 corner (12 square feet): 80 − 12 = 68 square feet. 80 ignores the missing corner, and 36 is the perimeter in feet, not an area.

The length is the distance from −3 to 5, which is 8 units, and the width is the distance from 2 to −4, which is 6 units. Area = 8 × 6 = 48 square units. 28 is the perimeter, and 4 comes from subtracting 3 from 5 and 2 from 4 without paying attention to the negative signs.

Volume = length × width × height = 2.5 × 1.5 × 4 = 3.75 × 4 = 15 cubic feet. 8 drops the fractions (2 × 1 × 4), and it is also the sum of the edges, which is not a volume.

Along each edge, two half-inch cubes fit in every inch: 4 cubes long, 2 wide and 6 tall, so 4 × 2 × 6 = 48 cubes. 6 is the volume in cubic inches, and 12 doubles it instead of multiplying by 8 (each cubic inch holds 2 × 2 × 2 = 8 small cubes).

The water forms a prism 50 cm by 30 cm by 25 cm: 50 × 30 × 25 = 37,500 cubic centimeters. 60,000 is the volume of the whole tank (using 40 cm), and 22,500 is the empty space above the water (15 cm deep).

The net has 6 squares, each with an area of 5 × 5 = 25 square centimeters, so the surface area is 6 × 25 = 150 square centimeters. 125 is the volume of the cube (5 × 5 × 5) in cubic centimeters, and 100 counts only 4 faces.

The box has three pairs of faces: 2 × (6 × 4) + 2 × (6 × 3) + 2 × (4 × 3) = 48 + 36 + 24 = 108 square inches. 72 is the volume, 84 leaves out the two 4 × 3 faces, and 54 counts each pair only once.

Base: 6 × 6 = 36. Each triangle: 12 × 6 × 5 = 15, and four triangles give 60. Total: 36 + 60 = 96 square inches. 156 forgets to halve the triangles, and 60 leaves out the base.

Filling a container measures the space inside it, which is volume in cubic units. Paint on walls and cardboard for a box are surface areas, and fencing around a garden is a perimeter.

The side from (1, 1) to (1, 7) is vertical with length 6, and the side from (1, 1) to (9, 1) is horizontal with length 8. They meet at a right angle, so area = 12 × 8 × 6 = 24 square units. 48 forgets to take half, and 14 adds the two legs.

The base area is 10 × 6 = 60 square inches. Since volume = base area × height, the height is 360 ÷ 60 = 6 inches. 36 divides by the length only, and 3.6 divides 360 by 100.

The parallelogram has area 10 × 6 = 60 square centimeters, and the triangle has half of that, 30 square centimeters. The difference is 60 − 30 = 30 square centimeters. 60 is the parallelogram's whole area, not the difference.