CBSE Class 5 Mathematics Shapes and Patterns Worksheet Set 01

Fill in the Blanks

Question. Nisha paints a large wooden block red; exactly _____ corner cubes have three faces painted red.
Answer: 8
Explanation: Every cube has 8 corners. Only the little cubes sitting right at the corners get paint on 3 of their sides.

Question. In an icosahedron, exactly _____ triangular faces meet at every vertex.
Answer: 5
Explanation: A vertex is just a pointy corner! In an icosahedron, 5 little triangle points touch each corner.

Question. Both an icosahedron and a dodecahedron have _____ straight edges in total.
Answer: 30
Explanation: An edge is the straight line where two flat faces meet. Even though their faces are shaped differently, both 3D solids have 30 lines.

Question. After creating a hollow 3 × 3 × 3 cube frame, exactly _____ small cubes have been removed.
Answer: 7
Explanation: A full solid cube has 27 small blocks (3 × 3 × 3 = 27). The frame keeps 20 blocks, so 27 − 20 = 7 blocks were taken out.

Question. In a painted 3 × 3 × 3 block, there are _____ small cubes that have only one face painted red.
Answer: 6
Explanation: A cube has 6 flat faces. The cube right in the middle of each face gets painted on only 1 side.

True or False

Question. Five squares can fit together around a point without any gaps or overlaps.
Answer: False
Explanation: Every corner of a square is 90 degrees. Four corners make a full turn of 360 degrees (90 × 4 = 360). Adding a fifth square makes 450 degrees, which is too big, so they will overlap!

Question. Three regular hexagons can fit together around a single point without any gaps.
Answer: True
Explanation: Each corner angle of a regular hexagon is 120 degrees. Three of them make 120 + 120 + 120 = 360 degrees, which fits together like a jigsaw puzzle!

Question. Regular octagons can fit together smoothly without any spaces to tile a flat floor.
Answer: False
Explanation: When you put regular octagons together side by side, their corners leave square gaps in between, so they cannot cover the floor completely on their own.

Question. A rectangle is considered a special type of parallelogram.
Answer: True
Explanation: A parallelogram is any four-sided shape with opposite sides that are parallel and equal. A rectangle has this too, plus all its corners are square right angles!

Question. In a dodecahedron, the identical number of faces meet at each vertex.
Answer: True
Explanation: A dodecahedron is a regular 3D shape, which means every single corner looks the same: exactly 3 pentagon faces meet at every point.

Questions / Short Question Answers

Question. How many distinct types of triangles can you make based on side lengths and angles?
Answer: 4 (Equilateral triangle, Isosceles triangle, Scalene triangle, and Right-angled triangle)
Explanation: Triangles can have all sides equal (equilateral), two sides equal (isosceles), no sides equal (scalene), or have a sharp square corner (right-angled).

Question. Nisha has glued 27 small cubes together to form a large cube and painted it red. How many small cubes have zero faces painted?
Answer: 1 small cube
Explanation: If you peel off all the outer blocks of the 3 × 3 × 3 cube, only 1 tiny cube hidden right in the middle stays untouched by paint.

Question. Tanu arranged 7 figures in a line using 2 squares, 2 triangles, 1 circle, 1 hexagon, and 1 rectangle. The square is between the circle and rectangle; the rectangle is between the square and triangle; the two triangles are next to the square; the hexagon is to the right of the triangle; the circle is to the left of the square. What is her arrangement?
Answer: Triangle, Circle, Square, Rectangle, Triangle, Hexagon (with the second square forming part of the pattern)
Explanation: Following the clues step-by-step from left to right puts the shapes in order so that every clue about their neighbors matches up.

Question. A 4 × 4 × 4 cube frame is made from tiny blocks. How many small cubes were removed to create the frame?
Answer: 32 small cubes
Explanation: A complete 4 × 4 × 4 block has 64 cubes (4 × 4 × 4 = 64). The outer frame uses 32 cubes, so 64 − 32 = 32 cubes were taken out.

Question. In a tiling pattern made of squares and triangles touching along edges, are the triangles equilateral? Why or why not?
Answer: Yes, the triangles are equilateral because each side of the triangle matches the equal side of the square.
Explanation: Because all four sides of a square are the same length, and each triangle side shares a side with the square, all three sides of the triangle must also be the same length.

Question. What 2D shapes form the faces of an icosahedron and a dodecahedron?
Answer: An icosahedron has equilateral triangles, and a dodecahedron has regular pentagons.
Explanation: An icosahedron is made of 20 flat 3-sided triangles, while a dodecahedron is made of 12 flat 5-sided pentagons.

Question. How many pieces are in a classic tangram set, and what shapes are they?
Answer: 7 pieces: 2 large right triangles, 1 medium right triangle, 2 small right triangles, 1 square, and 1 parallelogram.
Explanation: A tangram is an ancient puzzle made by cutting a single square into five triangles, one small square, and one slanted rectangle (parallelogram).

Question. When folding paper to form a kite shape, what shapes are formed inside?
Answer: Three right-angled triangles (with two of them being identical in size).
Explanation: Folding the flaps toward the diagonal crease divides the paper into sharp right-angled triangles that match on both sides.

Question. A 5 × 5 × 5 solid cube frame is made. How many small cubes were extracted from the full cube?
Answer: 81 small cubes
Explanation: A full 5 × 5 × 5 block contains 125 cubes (5 × 5 × 5 = 125). The hollow frame keeps 44 cubes, so 125 − 44 = 81 cubes were removed.

Match the Following

Question. Match each geometry statement with the appropriate shape it describes:

Explanation: Squares have equal sides and 90° corners. Rectangles have 90° corners with opposite sides equal. Rhombuses have equal sides with slanted corners, and parallelograms have opposite sides and opposite angles equal.

Vocabulary Activity - "Guess the Word"

Question. Guess the Word: I am a four-sided shape where two pairs of adjacent sides are equal in length, resembling a flying toy. What am I?
Answer: Kite
Explanation: A kite has two short sides next to each other that are equal, and two longer sides next to each other that are equal, just like the paper kites flown in the sky!

Question. Guess the Word: I am a three-dimensional solid figure with 12 flat faces, where each face is a regular pentagon. What am I?
Answer: Dodecahedron
Explanation: "Dodeca" means twelve in Greek! A dodecahedron looks like a 3D ball made of 12 five-sided pentagon patches.

Question. Guess the Word: I am an ancient Chinese puzzle made of seven flat geometric pieces that can be arranged to create different figures. What am I?
Answer: Tangram
Explanation: A tangram uses seven flat shapes (5 triangles, 1 square, 1 parallelogram) to make fun animals, people, and buildings.

Question. Guess the Word: I am a three-sided flat shape with every side having a different length. What am I?
Answer: Scalene triangle
Explanation: "Scalene" means uneven. In a scalene triangle, all three sides and all three angles are different from each other.

Question. Guess the Word: I am a repeating arrangement of shapes that fits together across a flat surface without leaving any gaps or overlaps. What am I?
Answer: Tessellation (or Tiling)
Explanation: Tessellation is like tiling a bathroom floor where tiles touch each other perfectly without any empty holes or overlapping edges.