UA · Unit 6 review

1. 1.

   Find the area of the parallelogram.

   Answer. 70 square cm

   A = b × h = 10 × 7 = 70 square cm.

2. 2.

   Find the volume of a 8 by 2 by 4 rectangular prism (cm).

   Answer. 64 cubic cm

   V = ℓwh = 8 × 2 × 4 = 64.

3. 3.

   A plane slices a right cylinder perpendicular to the base through the axis. What shape is the cross section?

   Answer. rectangle

   rectangle

4. 4.

   Two angles are complementary. One measures 23°. Find the other.

   Answer. 67°

   Complementary angles sum to 90°, so 90 − 23 = 67.

5. 5.

   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).

6. 6.

   Luis wraps a gift box 5 cm by 6 cm by 5 cm. Ignoring overlap, how much wrapping paper covers the whole surface?

   Answer. 170 square cm

   SA = 2(30 + 25 + 30) = 170 square cm.

7. 7.

   Elena packs 3 identical 7 by 4 by 7 cm boxes into a crate. What total volume do the boxes take?

   Answer. 588 cubic cm

   One box is 196. 3 boxes: 588 cubic cm.

8. 8.

   A plane slices a cube through three edges that meet at a vertex. What shape is the cross section? Write a complete answer — Owen will compare with a partner.

   Answer. triangle

   triangle

9. 9.

   Two angles are supplementary. One measures 63°. Find the other. Then Nora needs 4 of that amount. What is the total they need?

   Answer. 468°

   Supplementary angles sum to 180°, so 180 − 63 = 117. Then multiply by 4: 468°.

10. 10.

    Can a triangle have side lengths 6, 5, and 9? Write a complete answer — Grace will compare with a partner.

    Answer. yes

    Triangle inequality: 6 + 5 = 11 > 9.

11. 11.

    Think

    Sam used the slanted side 12 instead of the height 12 and got 120. What is the actual area of a parallelogram with base 10 in and height 12 in?

    Answer. 120 square in

    Height is perpendicular, not slanted. A = 10 × 12 = 120 square in.

12. 12.

    Think

    Sam added 3 + 8 + 3 = 14 for the volume of a 3 by 8 by 3 cm prism. What is the actual volume?

    Answer. 72 cubic cm

    Volume is the product: 3 × 8 × 3 = 72 cubic cm.

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