MATHS Answer the following (3 mark each)

Quadrilaterals whose opposite sides are equal are called parallelograms.
What types of angles do quadrilaterals A and B have? Which angles are equal in each of the above parallelograms?
In parallelogram A, opposite angles are equal.
In parallelogram B, all angles are equal and are right angles. Such a parallelogram is called a rectangle.
A rectangle is a special type of parallelogram.

This shape is called a kite.
What do you notice about the sides of a kite?
Side 1 = Side 2.
Similarly, Side 3 = Side 4.
These sides are called adjacent sides.
Here are two other possible quadrilaterals that are not kites.

No, five square cannot fit together perfectly around a point without any gaps or overlaps. Because, each angle of a square is a right angle. For shapes to fit perfectly around a point without gaps or overlaps (i.e., to form a tessellation around that point), the sum of the angles of the shapes meeting at that point must exactly equal to 4 right angles.
If we place five squares around a point, the sum of their angles would be 5 right angles which is greater than 4 right angles, so the squares would overlap.

(a) The full cube has 3 × 3 × 3 = 27 small cubes.
After removing the small cubes only the big cube frame are available, which has 20 small cubes.
So, total removed cubes = 27-20
= 7 cubes.
(b) The full cube has 4 × 4 × 4 = 64 small cubes.
After removing the small cubes the big cube frame has 32 small cubes.
So, total removed cubes = 64 – 32
= 32 cubes.
(c) The full cube has 5 × 5 × 5 = 125 small cubes.
After removing the small cubes the big cube frame has 44 small cubes.
So, total removed cubes = 125 – 44
= 81 cubes.

1. yes
2. 30
3. 12

1. equilateral triangles
2. yes
3. 5

1. yes
2. 30
3. 20

1. regular pentagon
2. yes
3. 3