This worksheet gives Grade 6 students ten problems on finding the area of right triangles, other triangles, parallelograms, trapezoids, and composite polygons. The problems start with direct use of a formula and move toward missing measurements and shapes cut into pieces.
The last three problems are word problems with dollars, paint, and pavers. Every problem practices Common Core standard 6.G.A.1. Show each formula, write the units, and check that every height is perpendicular to its base.
Problem 1: Right triangle
Find the area of a right triangle whose legs measure \(9\text{ ft}\) and \(4\text{ ft}\).
Problem 2: Triangle area
Find the area of a triangle with base \(14\text{ m}\) and height \(6\text{ m}\).
Problem 3: Parallelogram area
Find the area of a parallelogram with base \(12\text{ in}\) and height \(7\text{ in}\).
Problem 4: Missing height
A triangle has an area of \(45\text{ yd}^2\) and a base of \(10\text{ yd}\). Find its height.
Problem 5: Trapezoid area
Find the area of the trapezoid. Its parallel sides are \(6\text{ ft}\) and \(10\text{ ft}\), and its height is \(4\text{ ft}\).
Problem 6: Missing base
A parallelogram has an area of \(72\text{ cm}^2\) and a height of \(9\text{ cm}\). Find its base.
Problem 7: Rectangle plus triangle
Find the area of the polygon. A rectangle \(10\text{ ft}\) wide and \(6\text{ ft}\) tall has a triangle on top with base \(10\text{ ft}\) and height \(4\text{ ft}\).
Problem 8: Garden beds
Sofia’s garden bed is a trapezoid. The parallel sides are \(9\text{ m}\) and \(15\text{ m}\), and they are \(8\text{ m}\) apart. One bag of soil covers \(12\text{ m}^2\). How many bags does she need?
Problem 9: Painting a gable wall
A garage wall is a rectangle \(16\text{ ft}\) wide and \(8\text{ ft}\) tall, with a triangular peak above it. The peak has a base of \(16\text{ ft}\) and a height of \(5\text{ ft}\). One gallon of paint covers \(84\text{ ft}^2\) and costs \(\$32\). Find the total area of the wall and the cost of the paint for one coat.
Problem 10: Patio pavers
Jamal is paving an L-shaped patio. Before the corner is removed it is a \(14\text{ ft}\) by \(10\text{ ft}\) rectangle. A \(6\text{ ft}\) by \(4\text{ ft}\) rectangle is cut out of one corner. Pavers cost \(\$3.50\) per square foot. Find the area of the patio and the cost of the pavers.
See every chapter on the Grade 6 math page.