Area, Surface Area and Volume of Prisms: Grade 7 Math Test Answer Key – PDF Download

Question 1: Area of an L-shaped figure (3 points)

Split into a bottom rectangle \(14\times 5=70\) and a top rectangle \(8\times 4=32\): \(70+32=102\). Or subtract: \(14\times 9=126\) and \(126-6\times 4=102\).

\(102\text{ ft}^2\)

Scoring: 1 point for a valid way to break up (or complete) the figure; 1 point for correct partial areas; 1 point for \(102\text{ ft}^2\) with square units.

Question 2: Area of a pennant (2 points)

Rectangle: \(12\times 7=84\). Triangle: \(\frac{1}{2}\times 12\times 5=30\). Total: \(84+30=114\).

\(114\text{ in}^2\)

Scoring: 1 point for the rectangle area (84) and the triangle area (30); 1 point for the total with square units.

Question 3: Volumes of prisms (3 points)

1. \(9\times 6\times 4=216\): \(216\text{ in}^3\)
2. Base area: \(\frac{1}{2}\times 8\times 6=24\). Volume: \(24\times 11=264\): \(264\text{ cm}^3\)

Scoring: part (a) 1 point; part (b) 1 point for the base area, 1 point for the volume with cubic units.

Question 4: Surface area of a box (2 points)

\(2(10\times 6)+2(10\times 4)+2(6\times 4)=120+80+48=248\).

\(248\text{ cm}^2\)

Scoring: 1 point for finding all six faces (three pairs); 1 point for \(248\text{ cm}^2\) with square units.

Question 5: Surface area of a triangular prism (3 points)

Bases: \(2\times \frac{1}{2}\times 8\times 6=48\). Rectangles: \((8+6+10)\times 12=24\times 12=288\). Total: \(48+288=336\).

\(336\text{ cm}^2\)

Scoring: 1 point for the area of the two bases; 1 point for the three rectangular faces; 1 point for the total with square units.

Question 6: Missing height (2 points)

\(B=12\times 5=60\). Then \(60h=360\), so \(h=360: 60=6\).

\(6\text{ ft}\)

Scoring: 1 point for the base area (60) or a correct equation; 1 point for \(6\text{ ft}\).

Question 7: Volume of a composite solid (3 points)

Area of the L-shaped face: \(9\times 6-4\times 2=54-8=46\). Volume: \(46\times 5=230\).

\(230\text{ cm}^3\)

Scoring: 1 point for the area of the face (46); 1 point for multiplying by the depth; 1 point for \(230\text{ cm}^3\) with cubic units.

Question 8: Wrapping a gift (2 points)

Surface area: \(2(14\times 10)+2(14\times 6)+2(10\times 6)=280+168+120=568\text{ in}^2\).

Since \(568\le 600\), one sheet is enough, with \(32\text{ in}^2\) left over.

Scoring: 1 point for the surface area (568); 1 point for comparing with 600 and answering yes.

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