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SubjectFree lesson

Plane figures 1

ClassNotes Team 3 MIN READUPDATED 4 JUL 2026

BASIC SCIENCE JSS2 Second term

Sub-Theme: Drawing practice

WEEK 1

Plane figures 1

Performance objectives

Students should be able to:

  1. Identify regular plane figures.
  2. Construct regular plane figures of equal areas.

Content

Plane figures

The idea of an area may be explained as the amount of space enclosed within the boundary of a figure. For instance, the area of the floor of a classroom is the amount of space enclosed within the four corners of the room. Also, the area of the top of the teacher's table is the amount of space enclosed within the edges of the table. 

To measure the amount of space, we determine the number of square units. As an example, let us find the area of the rectangular floor of length 10cm and width 6cm. To do this, one method may be to take square cardboard of one-centimeter side starting from one corner of the floor, mark the outline of the cardboard, edge to edge, until the whole space of the floor is covered. Then the number of one squared centimeter marking is counted and that gives the area of the floor in square meters.

To construct a triangle equal area to a given triangle

a.) When the triangle is on equal bases

  1. Draw a given triangle ABC and produce the base AB to D making DE=AB
  2. Though C, draw CF parallel to AD
  3. With center E and radius equal to a side of the required triangle, cut CF at G

To construct a triangle equal in area to any given parallelogram

  1. Draw the parallelogram ABCD and draw diagonal BD.
  2. Through C, draw a line parallel to DB, and intersect AB produced at E.
  3. Join DE. Triangle AED is the required triangle.

To construct a rectangle equal in area to a given rectangle of different length

  1. Draw the given rectangle ABCD.
  2. On AB (produced), mark off AE equal to the different length of the required rectangle.
  3. Join DE
  4. Through B, draw a line parallel to ED to intersect AD (produced) at F. AF is the width of the required rectangle AEGF.

To construct a square in the area to a given rectangle

  1. Draw a given rectangle ABCD.

With center B and radius BC, swing arc CE to intersect AB produced at E.

  1. Bisect AE in F and draw a semicircle AE on diameter.
  2. Produce BC to meet semi-circle at G. BG is the size of the required square.
  3. Complete square BGHI.

To construct a square equal in area to the sum of area two given squares

  1. Draw a line and mark off AB equal to the sides of one of the given squares.
  2. At A, erect a perpendicular and mark off AC equal to the side of the other square 
  3. Complete the required square CBD.

Note: this is based on the Pythagoras theorem which states that the square of the hypotenuse of a right-angle triangle is equal to the sum of the squares of the other two sides.