Class 5 Advanced Geometry Worksheet PDF: Area, Volume, Angles & Coordinate Geometry

Comprehensive Class 5 geometry worksheet covering area formulas, volume of 3D shapes, angle relationships, and coordinate plotting. 24 challenging problems with real-world applications and complete solutions.

Advanced Geometry Concepts for Class 5

Area (2D Shapes)

Square: Area = side × side = side²

Rectangle: Area = length × width

Triangle: Area = ½ × base × height

Area is measured in square units (cm², m², km²)

Volume (3D Shapes)

Cube: Volume = side × side × side = side³

Cuboid: Volume = length × width × height

Volume is measured in cubic units (cm³, m³)

Angles

Complementary Angles: Two angles that add up to 90°

Supplementary Angles: Two angles that add up to 180°

Adjacent Angles: Angles that share a common vertex and side

Vertically Opposite Angles: Equal angles formed when two lines intersect

Coordinate Geometry Basics

Points are located using ordered pairs (x, y)

x-axis = horizontal line, y-axis = vertical line

Origin = point (0, 0) where axes meet

Special Properties

Sum of angles in a triangle = 180°

Sum of angles in a quadrilateral = 360°

Diagonal of a rectangle divides it into two equal triangles

Solved Example

Problem: Find the area of a rectangle with length 12 cm and width 8 cm.

Solution:

Area = length × width

Area = 12 cm × 8 cm

Area = 96 cm²

Answer: The area is 96 square centimeters!

Sample Practice Problems

Find the area of a square with side 6 cm.

Find the area of a triangle with base 10 cm and height 6 cm.

A rectangular garden is 15 m long and 8 m wide. Find the perimeter, area, and if grass costs ₹10 per m², how much will it cost to cover the entire garden?

Find the volume of a cuboid with length 8 cm, width 5 cm, and height 3 cm.

A square field has an area of 144 m². What is the length of each side?

A rectangular room is 6 m long and 4 m wide. The floor needs to be covered with square tiles of side 50 cm. How many tiles are needed?

A rectangular park is 80 m long and 60 m wide. A path 2 m wide runs around the inside of the park. Find the area of the path.

The coordinates of three vertices of a rectangle are A(2, 3), B(8, 3), and C(8, 7). Find the coordinates of the fourth vertex D, length, width, and area of the rectangle.

A water tank in the shape of a cuboid is 2 m long, 1.5 m wide, and 1 m high. How many liters of water can it hold? (1 m³ = 1000 liters)

Scoring Guide

20-24 correct: Excellent! Outstanding performance! Start learning about circles, explore more coordinate geometry, study geometric constructions, learn about surface area of 3D shapes, and begin exploring ratio and proportion in geometry.

15-19 correct: Very Good! Great job! Practice area and volume problems daily. Master angle relationships. Work on word problems involving area and perimeter. Practice plotting points on coordinate grids.

10-14 correct: Good Effort! Good start! Memorize area formulas. Practice volume calculations for cube and cuboid. Understand angle relationships thoroughly. Start with simpler coordinate geometry problems.

0-9 correct: Keep Trying! Don't give up! Master perimeter first before moving to area. Learn one formula at a time. Use graph paper to understand area visually. Practice basic angle facts.

Tips for Mastering Class 5 Geometry

Area Formulas: Square = side², Rectangle = length × width, Triangle = ½ × base × height. Remember: Area is always in square units.

Volume Formulas: Cube = side³, Cuboid = length × width × height. Remember: Volume is always in cubic units.

Angle Relationships: Complementary angles add to 90°, Supplementary angles add to 180°, Vertically opposite angles are always equal, Angles in a triangle add to 180°, Angles in a quadrilateral add to 360°.

Coordinate Geometry: Points are written as (x, y), x tells you how far right, y tells you how far up, Origin is at (0, 0).

Problem-Solving Strategy: Read carefully twice, draw a diagram if not given, write down the formula, substitute the values, calculate step by step, check if your answer makes sense.

Unit Conversion: 1 m = 100 cm so 1 m² = 10,000 cm², 1 m³ = 1,000,000 cm³, 1 m³ = 1,000 liters. Always convert to the same units before calculating.

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