MIA · Mixed set · Unit 6

1. 1.

   Find the area of the parallelogram.

   Answer. 28 square cm

   A = b × h = 7 × 4 = 28 square cm.

2. 2.

   Find the volume of a 5 by 2 by 2 rectangular prism (cm).

   Answer. 20 cubic cm

   V = ℓwh = 5 × 2 × 2 = 20.

3. 3.

   A plane slices a cube through three edges that meet at a vertex. What shape is the cross section?

   Answer. triangle

   triangle

4. 4.

   Two angles are supplementary. One measures 65°. Find the other.

   Answer. 115°

   Supplementary angles sum to 180°, so 180 − 65 = 115.

5. 5.

   Can a triangle have side lengths 6, 5, and 13? Write a complete answer — Ava will compare with a partner.

   Answer. no

   Triangle inequality: 6 + 5 = 11 ≤ 13.

6. 6.

   Owen wraps a gift box 7 cm by 6 cm by 6 cm. Ignoring overlap, how much wrapping paper covers the whole surface?

   Answer. 240 square cm

   SA = 2(42 + 42 + 36) = 240 square cm.

7. 7.

   Sam packs 3 identical 5 by 5 by 6 cm boxes into a crate. What total volume do the boxes take?

   Answer. 450 cubic cm

   One box is 150. 3 boxes: 450 cubic cm.

8. 8.

   A plane slices a right cylinder parallel to the base. What shape is the cross section? Write a complete answer — Ava will compare with a partner.

   Answer. circle

   circle

9. 9.

   Two angles are supplementary. One measures 84°. Find the other. Then Priya needs 3 of that amount. What is the total they need?

   Answer. 288°

   Supplementary angles sum to 180°, so 180 − 84 = 96. Then multiply by 3: 288°.

10. 10.

    Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique? Write a complete answer — Mei will compare with a partner.

    Answer. yes (SAS)

    Two sides and the included angle determine a unique triangle (SAS).

11. 11.

    Think

    Sam used the slanted side 15 instead of the height 10 and got 195. What is the actual area of a parallelogram with base 13 m and height 10 m?

    Answer. 130 square m

    Height is perpendicular, not slanted. A = 13 × 10 = 130 square m.

12. 12.

    Think

    Mei added 6 + 7 + 3 = 16 for the volume of a 6 by 7 by 3 cm prism. What is the actual volume?

    Answer. 126 cubic cm

    Volume is the product: 6 × 7 × 3 = 126 cubic cm.

Original extra practice. Keys are computed from the items, not guessed.