Area, Surface Area, and Volume: math practice, Grade 6 – download the PDF

1 Area of a triangle ★★★

A triangular sail has a base of 12 cm and a height of 7 cm. Find its area.

2 Area of a parallelogram ★★★

A parallelogram-shaped garden bed has a base of 15 in and a height of 6 in. The slanted side measures 8 in. Find the area.

3 True or false: triangle area ★★★

Leo says: “A triangle with base 10 m and height 6 m has an area of 60 m².” Is he right? Explain.

4 Area of a trapezoid ★★★

A trapezoid has bases of 5 cm and 9 cm and a height of 4 cm. Find its area.

5 Rectangle on a grid ★★★

Plot the points \( (2, 1) \), \( (8, 1) \), \( (8, 5) \), and \( (2, 5) \) on a coordinate plane and join them in order. What shape do you get, and what is its area?

6 Name the solid from its net ★★★

Name the solid that each net folds into.

1. 6 congruent squares
2. 1 square and 4 triangles
3. 2 triangles and 3 rectangles

7 Volume of a box ★★★

A box is 8 cm long, 5 cm wide, and 3 cm tall. Find its volume.

8 Finding a missing height ★★★

A triangular piece of land has an area of 54 m² and a base of 12 m. What is its height?

9 Mulch for a flower bed ★★★

A flower bed is a parallelogram with base 3.5 m and height 2 m. One bag of mulch covers 1.75 m². How many bags are needed to cover the whole bed?

10 A trapezoid sail ★★★

A sail is a trapezoid with parallel sides of 4 ft and 6 ft that are 3.5 ft apart. Fabric costs $4 per square foot. How much does the fabric for the sail cost?

11 Carpeting a room ★★★

A room is a 9 m by 6 m rectangle with a 4 m by 3 m alcove attached to one wall. Carpet costs $12 per square meter. What does it cost to carpet the room and the alcove?

12 Triangle on the coordinate plane ★★★

A triangle has vertices \( A(1, 2) \), \( B(7, 2) \), and \( C(4, 8) \). Find its area.

13 Wrapping a cube ★★★

A cube-shaped gift box has edges of 7 cm. How much paper is needed to cover all of its faces, with no overlap?

14 A box with mixed numbers ★★★

A box is \( 3\dfrac{1}{2} \) in long, 2 in wide, and \( 1\dfrac{1}{2} \) in tall. Find its volume.

15 Gift box surface area ★★★

A rectangular box is 12 cm long, 5 cm wide, and 4 cm tall. (a) Find its surface area. (b) Its lid and bottom are not painted. How much area is painted?

16 A square pyramid ★★★

A square pyramid has a base of 10 cm by 10 cm. Each triangular face has a slant height of 13 cm. Find (a) the lateral area and (b) the total surface area.

17 The camping tent ★★★

A tent is a triangular prism. Each triangular end has a base of 6 ft and a height of 4 ft, the two sloping sides are 5 ft wide, and the tent is 9 ft long. (a) Find the area of the fabric for the two sloping sides and the two ends (no floor). (b) Find the total surface area including the floor.

18 A swallowtail banner ★★★

A banner is a rectangle 18 cm long and 10 cm tall. A triangular notch is cut from one short end: the notch has a base of 10 cm (the whole short side) and a depth of 4 cm. Find the area of the banner that remains.

19 An L-shaped polygon on the grid ★★★

A polygon has vertices \( A(1, 1) \), \( B(7, 1) \), \( C(7, 4) \), \( D(4, 4) \), \( E(4, 7) \), and \( F(1, 7) \). (a) Find the length of each side. (b) Find the perimeter. (c) Find the area.

20 Water in a fish tank ★★★

A fish tank is \( 2\dfrac{1}{2} \) ft long, \( 1\dfrac{1}{2} \) ft wide, and 2 ft tall. It is filled with water to \( \dfrac{3}{4} \) of its height. (a) Find the volume of the tank. (b) Find the volume of the water.

21 Same base, same height ★★★

Triangle 1 has vertices \( (0, 0) \), \( (8, 0) \), and \( (2, 5) \). Triangle 2 has vertices \( (0, 0) \), \( (8, 0) \), and \( (6, 5) \). Without drawing, explain why they have the same area, then find it.