Solids, angles and quadrilaterals worksheet

Part A: Working out and filling in

1. 1. 18 faces

   First count the faces of one prism on a 4-sided base: how many side faces, and how many bases top and bottom?

   Each has 4 side faces and 2 bases, 6 faces; 3 of them have 18.

2. 2. 10 segments

   Start at the leftmost point and count how many points to its right it can join; do the same for each point and add.

   Count to the right from each point and add: 10 in all.

3. 3. 15 angles

   Cutting off a corner loses that angle, but new ones appear at the ends of the cut. Work out one sheet first.

   Each loses 1 angle but gains 2 at the ends of the cut: 4 − 1 + 2 = 5; 3 sheets have 15.

4. 4. 4 right angles

   Check each corner with a set square; only an exact match is a right angle.

   Check each corner with a set square: 4 right angles.

5. 5. 50 cm

   A rectangle's opposite sides are equal, so there are two sides of 12 cm and two of 13 cm.

   Opposite sides are equal: 12 + 13 + 12 + 13 = 50.

Part B: Choose, or true or false

1. 6. False

   A prism has one side face for each side of its base. Do the two bases count as sides? Then compare with 5.

   Each of the base's 3 sides has a side face: 3 of them (the two bases aren't sides).

2. 7. True

   How many sides does one quadrilateral have? Multiply by 3, then compare with 12.

   Each has 4 sides, so 3 have 12.

3. 8. B

   An angle has one vertex, with two straight sides drawn from it. Check each picture.

   An angle has a vertex and two straight sides drawn from it.

4. 9. D

   A right angle is like the corner of a book. Check each one with a set square.

   Check with a set square: the one that matches its corner exactly is the right angle.

5. 10. C. PC

   Of the segments from P to the line, which meets it at a right angle? The slanting ones are longer.

   The segment perpendicular to the line is the shortest.

6. 11. D. 12 cm

   The perpendicular is the shortest, so is any other segment from P to the line longer or shorter than 8 cm?

   The perpendicular is shortest; any other segment is longer than 8 cm.

7. 12. False

   Only the dots are end points, not the arrows. Count the dots and compare with 1.

   An end point is where it stops, drawn as a dot; an arrow means it goes on, and is not an end point.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 21 faces

   Count the faces of one pyramid on a 6-sided base first: the side faces plus one base. Then think about 3 of them.

   Each has 6 + 1 = 7 faces, so 3 have 21.

2. 14. D. Route 2

   Between two points, what kind of path is shortest? Look for the route that doesn't bend.

   Between two points the segment is shortest: take the straight route.

3. 15. 5 big steps

   Count from 12 to 5 clockwise, then anticlockwise, and take the smaller count.

   The minute hand on 12, the hour hand on 5; counting both ways, the smaller is 5.

4. 16. B. Obtuse

   Hold a set square against it: is the angle smaller than, the same as, or bigger than a right angle?

   Compare with a right angle: smaller is acute, equal is right, bigger is obtuse.

5. 17. 3 bars

   Draw it: how many bars run across between 2 rows? Don't forget the frame along the top and bottom.

   Horizontal bars run between the 2 rows and along the top and bottom: 2 + 1 = 3. The vertical bars number 3 + 1 = 4.

6. 18. 8 matches

   A square has 4 equal sides, each using 2 matches.

   A square has 4 equal sides: 4 lots of 2 is 8.