This answer key gives a full worked solution and a scoring guide for each of the nine questions. The test is worth 20 points. Award partial credit as described, and look for units on every area, since a correct number without square units loses the final point.
Question 1: Triangles (2 points)
- \(A = \frac{1}{2} \times 15 \times 8 = 60\). The area is \(60\text{ in}^2\).
- \(A = \frac{1}{2} \times 11 \times 6 = 33\). The area is \(33\text{ m}^2\).
Scoring: 1 point for each part. Award the point for a correct value with square units; give half credit if the factor \(\frac{1}{2}\) is used but the arithmetic is wrong.
Question 2: Parallelogram (2 points)
The slanted side is not used. \(A = bh = 18 \times 7 = 126\).
The area is \(126\text{ ft}^2\).
Scoring: 1 point for choosing base 18 and height 7 (not 10); 1 point for the correct area with units.
Question 3: Trapezoid (2 points)
\(A = \frac{1}{2}(7 + 13)(5) = \frac{1}{2} \times 20 \times 5 = 50\).
The area is \(50\text{ cm}^2\).
Scoring: 1 point for adding the bases and using the factor \(\frac{1}{2}\); 1 point for the correct area with units.
Question 4: Missing base (2 points)
\(54 = \frac{1}{2} \times b \times 9\), so \(54 = 4.5b\).
\(b = 54 : 4.5 = 12\)
The base is \(12\text{ ft}\).
Scoring: 1 point for a correct equation; 1 point for solving it correctly with units.
Question 5: Rhombus (2 points)
- Each leg is half a diagonal: \(5\text{ in}\) and \(3\text{ in}\). \(A = \frac{1}{2} \times 5 \times 3 = 7.5\). The area is \(7.5\text{ in}^2\).
- \(4 \times 7.5 = 30\). The area is \(30\text{ in}^2\).
Scoring: 1 point for each part. In part (b), accept \(30\text{ in}^2\) found by any valid method.
Question 6: Composite polygon (3 points)
Cut off the right triangle at the right end. Its legs are \(14 – 10 = 4\text{ ft}\) and \(6\text{ ft}\).
Rectangle: \(10 \times 6 = 60\text{ ft}^2\). Triangle: \(\frac{1}{2} \times 4 \times 6 = 12\text{ ft}^2\).
Total: \(60 + 12 = 72\). Check with the trapezoid formula: \(\frac{1}{2}(10 + 14)(6) = 72\).
The area is \(72\text{ ft}^2\).
Scoring: 1 point for a valid decomposition and the leg lengths; 1 point for the two piece areas; 1 point for the correct total with units.
Question 7: Market tarp (3 points)
- Rectangle: \(20 \times 12 = 240\text{ ft}^2\). Triangle: \(\frac{1}{2} \times 6 \times 4 = 12\text{ ft}^2\). Left: \(240 – 12 = 228\). The area is \(228\text{ ft}^2\).
- \(228 \times \$0.75 = \$171\). The cost is \(\$171\).
Scoring: Part (a): 1 point for both piece areas, 1 point for subtracting correctly. Part (b): 1 point.
Question 8: Find the error (2 points)
Liam multiplied the base and height but did not take half. A triangle is half of a parallelogram with the same base and height.
\(A = \frac{1}{2} \times 10 \times 7 = 35\). The correct area is \(35\text{ ft}^2\).
Scoring: 1 point for identifying the missing factor \(\frac{1}{2}\); 1 point for the correct area with units.
Question 9: Equal areas (2 points)
Parallelogram: \(8 \times 5 = 40\text{ m}^2\).
Triangle: \(40 = \frac{1}{2} \times 10 \times h = 5h\), so \(h = 8\).
The height is \(8\text{ m}\).
Scoring: 1 point for the area \(40\text{ m}^2\); 1 point for the correct height with units.
20 points
See every chapter on the Grade 6 math page.