This 45-minute test checks Grade 6 skills on the area of triangles, parallelograms, trapezoids, and composite polygons. It has nine questions worth 20 points in all. Show your work and include the correct square units in every answer.
- Grade: Grade 6
- Chapter: Area of Triangles, Quadrilaterals and Polygons
- Common Core: 6.G.A.1
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 2 pts)
Question 1: Triangles (2 points)
- Find the area of a right triangle with legs \(15\text{ in}\) and \(8\text{ in}\). (1 point)
- Find the area of a triangle with base \(11\text{ m}\) and height \(6\text{ m}\). (1 point)
Question 2: Parallelogram (2 points)
A parallelogram has a base of \(18\text{ ft}\), a slanted side of \(10\text{ ft}\), and a height of \(7\text{ ft}\). Find its area.
Question 3: Trapezoid (2 points)
A trapezoid has parallel sides of \(7\text{ cm}\) and \(13\text{ cm}\) and a height of \(5\text{ cm}\). Find its area.
Question 4: Missing base (2 points)
A triangle has an area of \(54\text{ ft}^2\) and a height of \(9\text{ ft}\). Find the length of its base.
Question 5: Rhombus (2 points)
The diagonals of a rhombus cut it into four congruent right triangles. The diagonals measure \(10\text{ in}\) and \(6\text{ in}\) and cross at their midpoints.
- Find the area of one triangle. (1 point)
- Find the area of the rhombus. (1 point)
Question 6: Composite polygon (3 points)
Find the area of the polygon shown. The top side is \(10\text{ ft}\), the bottom side is \(14\text{ ft}\), and the left side is \(6\text{ ft}\) and perpendicular to both.
Question 7: Market tarp (3 points)
A farmers market stall has a rectangular tarp \(20\text{ ft}\) by \(12\text{ ft}\). A right triangle with legs \(6\text{ ft}\) and \(4\text{ ft}\) is cut off one corner.
- Find the area of the tarp that is left. (2 points)
- New tarp costs \(\$0.75\) per square foot. Find the cost of a tarp with that area. (1 point)
Question 8: Find the error (2 points)
Liam says a triangle with base \(10\text{ ft}\) and height \(7\text{ ft}\) has an area of \(70\text{ ft}^2\). Explain his mistake and find the correct area.
Question 9: Equal areas (2 points)
A parallelogram has a base of \(8\text{ m}\) and a height of \(5\text{ m}\). A triangle has the same area and a base of \(10\text{ m}\). Find the height of the triangle.
See every chapter on the Grade 6 math page.