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How do you derive the formulae for the area of LEARNING
various shapes? STANDARDS
Derive the formulae of
2 Group the area of triangles,
parallelograms, kites and
trapeziums based on the
Aim: To derive the formula for the area of triangles. area of rectangles.
Instruction: Perform the activity in groups of four.
1. Referring to Diagram (a) as shown, D a C
(a) is the area of ∆ABD the same as the area of
∆BCD? b
(b) state the area of rectangle ABCD in terms of a
and b.
(c) hence, state the area of ∆ABD in terms of a A B
and b. Diagram (a)

2. Referring to Diagram (b) as shown, a
(a) state the area of ∆BFE in terms of b and c D E C
based on rectangle BFEC.
(b) state the area of ∆AFE in terms of b and d b
based on rectangle AFED.

(c) the area of ∆ABE = + A d F c B

= 1 b Diagram (b)
1
2
2
= Distributive law

3. Referring to Diagram (c) as shown, D a C E
CHAPTER
10 (a) what is the length of DE in terms of a and c?
(b) state the area of ∆AFE in terms of a, b and c b
based on rectangle AFED.

(c) state the area of ∆BFE in terms of b and c A B c F
based on rectangle BFEC.
Diagram (c)
(d) hence the area of ∆ABE = area of ∆AFE – area of ∆BFE

2
1
= 1 b –
2
= 1 ba + –
2

Distributive law

232
Chapter 10

10 TB Math F1.indd 232 11/10/16 12:19 PM