# Mensuration

## Overview

Mensuration is a fundamental topic in Geometry and Trigonometry that deals with the measurement of geometric figures and their properties. This branch of mathematics is essential for calculating perimeters, areas, volumes, and distances in various real-world applications.

One of the primary objectives of studying mensuration is to be able to calculate the perimeters and areas of different geometric shapes such as triangles, quadrilaterals, circles, and composite figures. Understanding how to determine these measurements is crucial in fields like architecture, engineering, and physics.

When it comes to circles, mensuration involves finding the length of arcs and chords, as well as calculating the perimeters and areas of sectors and segments. These calculations are significant in fields like surveying and construction where circular structures and spaces need precise measurements.

Furthermore, mensuration extends to calculating the total surface areas and volumes of various simple solids like cuboids, cylinders, cones, pyramids, prisms, spheres, and composite figures. Being able to determine these measurements accurately is vital for tasks such as packaging design, material estimation, and 3D modeling.

Lastly, mensuration also plays a role in determining the distance between two points on the Earth's surface. Understanding concepts like longitudes and latitudes is essential for navigation, geography, and cartography. Being able to calculate distances accurately on a spherical surface is crucial for global positioning and mapping applications.

Overall, a solid understanding of mensuration is essential for anyone working with shapes, sizes, and measurements in various disciplines. Mastering the calculations involved in perimeters, areas, volumes, and distances enables individuals to solve complex real-world problems and make informed decisions based on accurate mathematical data.

## Objectives

1. Calculate Surface Areas and Volumes of Simple Solids and Composite Figures
2. Determine Distance Between Two Points on the Earth's Surface
3. Find Perimeters and Areas of Sectors and Segments of Circles
4. Calculate Perimeters and Areas of Plane Geometrical Figures
5. Determine Lengths of Arcs and Chords of a Circle

## Lesson Note

Mensuration is a branch of mathematics that deals with the measurement of geometric figures and their parameters like length, area, volume, and perimeter. It is an essential topic as it finds applications in various fields such as engineering, architecture, and daily activities. This guide will help you understand the concepts related to mensuration and how to calculate the necessary parameters for different shapes and figures.

## Lesson Evaluation

Congratulations on completing the lesson on Mensuration. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

1. Find the area of a triangle with base 6 cm and height 8 cm. A. 14 cm² B. 24 cm² C. 28 cm² D. 48 cm² Answer: B. 24 cm²
2. Calculate the perimeter of a rectangle with sides measuring 12 cm and 8 cm. A. 28 cm B. 40 cm C. 48 cm D. 56 cm Answer: B. 40 cm
3. Determine the circumference of a circle with radius 5 cm. A. 10π cm B. 15π cm C. 20π cm D. 25π cm Answer: A. 10π cm
4. What is the area of a square with each side measuring 10 cm? A. 40 cm² B. 60 cm² C. 80 cm² D. 100 cm² Answer: D. 100 cm²
5. Calculate the surface area of a cube with each side measuring 4 cm. A. 64 cm² B. 96 cm² C. 128 cm² D. 256 cm² Answer: D. 96 cm²
6. Determine the volume of a cylinder with height 10 cm and radius 3 cm. A. 30π cm³ B. 90π cm³ C. 60π cm³ D. 100π cm³ Answer: 90π cm³
7. Find the area of a trapezium with bases 5 cm and 7 cm, and height 4 cm. A. 20 cm² B. 24 cm² C. 28 cm² D. 32 cm² Answer: B. 24 cm²
8. Calculate the volume of a cone with radius 6 cm and height 9 cm. A. 54π cm³ B. 72π cm³ C. 108π cm³ D. 162π cm³ Answer: A. 54π cm³
9. Determine the total surface area of a square pyramid with base side 8 cm and slant height 10 cm. A. 160 cm² B. 240 cm² C. 320 cm² D. 400 cm² Answer: B. 240 cm²
10. What is the volume of a sphere with radius 5 cm? A. 100π cm³ B. 125π cm³ C. 150π cm³ D. 175π cm³ Answer: A. 100π cm³

## Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Mensuration from previous years

Question 1

The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.

Question 1

In the figure, PQ\\SR, ST\\, ST\\RQ, PS = 7cm, PT = 7cm, SR = 4cm. Find the ratio of the area QRST to the area of PQRS.

Question 1

The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.

Practice a number of Mensuration past questions