This worksheet has 20 problems on area, volume, and surface area, aligned with Common Core standard 7.G.B.6. The first problems ask for the area of parallelograms, triangles, trapezoids, and composite figures, followed by volume and surface area of cubes, rectangular prisms, and triangular prisms.
The last problems are word problems with composite solids, a toy chest, a pool, and a tent. Draw the pieces, label every dimension, and give each answer with square or cubic units.
Problem 1: Parallelogram and triangle
Find the area of each shape. The dashed segments show the heights.
- The parallelogram
- The triangle
Problem 2: Volume of a rectangular prism
Find the volume of the box.
Problem 3: Cube surface and volume
A cube-shaped storage bin has edges of \(7\text{ ft}\). Find its surface area and its volume.
Problem 4: Area of a trapezoid
Find the area of the trapezoid.
Problem 5: Trapezoid ramp
The side view of a wheelchair ramp platform is a trapezoid. Its parallel sides are \(9\text{ ft}\) and \(15\text{ ft}\), and the distance between them is \(6\text{ ft}\). Find its area.
Problem 6: Area of an L-shape
Find the area of the L-shaped patio.
Problem 7: Lawn with a pool
A backyard lawn is a \(20\text{ ft}\) by \(12\text{ ft}\) rectangle. A \(5\text{ ft}\) by \(4\text{ ft}\) rectangular pool sits inside it. Find the area of the grass.
Problem 8: Rectangle and triangle
A banner is a rectangle with a triangle on top. Find its area.
Problem 9: Volume of a triangular prism
Find the volume of the triangular prism.
Problem 10: Right triangle prism
The base of the prism is a right triangle with legs \(7\text{ in}\) and \(6\text{ in}\). The prism is \(8\text{ in}\) long. Find its volume.
Problem 11: Surface area of a box
A shoe box is \(12\text{ in}\) long, \(7\text{ in}\) wide, and \(5\text{ in}\) tall. Find the surface area of the closed box.
Problem 12: Surface area from a net
The net folds into a closed box that is \(6\text{ in}\) long, \(4\text{ in}\) wide, and \(3\text{ in}\) tall. Find the surface area of the box.
Problem 13: Surface area of a triangular prism
Find the surface area of the prism. The bases are right triangles.
Problem 14: Missing prism length
The base of a triangular prism is a triangle with base \(10\text{ cm}\) and height \(6\text{ cm}\). The volume of the prism is \(270\text{ cm}^3\). Find the length of the prism.
Problem 15: Missing dimension
A rectangular fish tank is \(24\text{ in}\) long and \(10\text{ in}\) wide. It holds \(3{,}600\text{ in}^3\) of water when full. How tall is the tank?
Problem 16: Painting a toy chest
Ethan paints the outside of a toy chest, including the lid but not the bottom. The chest is a rectangular prism \(4\text{ ft}\) long, \(2\text{ ft}\) wide, and \(2\text{ ft}\) tall. One can of paint covers \(16\text{ ft}^2\) and costs $9. Find the area to paint and the cost of the paint.
Problem 17: Volume of a composite solid
A concrete step block has an L-shaped front face. Find its volume.
Problem 18: House-shaped solid
A model house is a rectangular prism topped by a triangular prism roof. The rectangular part is \(6\text{ ft}\) wide, \(4\text{ ft}\) tall, and \(10\text{ ft}\) long. The roof has triangular ends with base \(6\text{ ft}\) and height \(3\text{ ft}\), and it is also \(10\text{ ft}\) long. Find the total volume.
Problem 19: Tiling a pool
A community pool is a rectangular prism \(20\text{ ft}\) long, \(10\text{ ft}\) wide, and \(5\text{ ft}\) deep. Maya’s town tiles the floor and the four inside walls. Tile costs $3 per square foot. (a) Find the volume of the pool. (b) Find the area to be tiled. (c) Find the cost of the tile.
Problem 20: Tent problem
Aisha is making a tent shaped like a triangular prism. The triangular ends have base \(6\text{ ft}\) and height \(4\text{ ft}\). The slanted sides are \(5\text{ ft}\) long, and the tent is \(8\text{ ft}\) long.
- Find the volume of the tent.
- Find the amount of fabric needed for the two triangular ends and the two slanted sides (no floor).
See every chapter on the Grade 7 math page.