This document discusses calculating the area of triangles. It explains that the area of a triangle is 1/2 * base * height. It provides formulas to calculate the area using two sides and the included angle. Examples are given to demonstrate calculating areas when given side lengths and angles. The document also discusses a problem involving finding the area of a triangle within a three-dimensional pyramid structure. Formulas for trigonometric functions are reviewed.

1. 10.3 The Area Of A Triangle Prepared By, AsnitaMapasisi NurulHanisahHalbani SharmizaAdlinaJunaidi

2. 10.3.1 Area Of A Triangle Consider a triangle ABC on the right. By dropinga perpendicular line, h from C to meet AB at D, sin A = h/b , h = b sin A CArea of triangle = ½ x base x height = ½ x c x h = ½ c x b sin A b h a = ½ bcsin A A D B c Area of ∆ABC = ½ bc sin A

3. 10.3.1 Area Of A Triangle Similarity,area of ∆ABC = ½ ac sin B or ½ absin C. Hence,to find the area of a triangle ABC given two sides and the included angle is as follows : Area of ABC = ½ bcsin A = ½ ac sin B = ½ absin C

4. 10.3.1 Area Of A Triangle Example 5 Find the areas of the following triangles. a ) 3cm A 5 cm B b ) C 8 cm A B C 32̊ 55 ˚ 10 cm

5. 10.3.1Area Of A Triangle Solution : a ) Area of ∆ ABC = ½ bcsin A = ½ (3)(5) sin 32 = 3.97 cm² b ) By using the sine rule b = c b = 40˚ 57’ sin b sin c = 180˚ - 55˚- 40˚57’ 8 = 10 = 84˚3’ sin bsin 55˚ sin b = 8 ( sin 55˚ ) ABC = ½ bcsin A 10 = ½ (8)(10) sin 84˚3’ = 39.78 cm²

6. 10.3.2Problems Involving Three Dimensions Example 6 The diagram on the right shows a pyramid of height 9 cm and stands on a square base of 12 cm.The vertex V is vertically above the point D and U is the midpoint of BC.Calculate, A ) UAV B ) the area of ∆UAV 9 cm V D C U A 12 cm 12 cm B

7. 10.3.2 Problems Involving Three Dimensions Solution : U V A B D U V 6 cm 9 cm 9 cm A D 12 cm 12 cm 13.416 cm AU ² = 6² + 12² = 180 AU = 13.416 cm DU = AU = 13.416 UV ² = 9² + 13.416² = 260.989 UV = 16.155 cm AV ² = 9² + 12² = 225 AV = 15 cm

8. 10.3.2 Problems Involving Three Dimensions b ) Area ∆ UAV = ½ (13.416) (15) sin 69˚2’ = 93.958 cm² V 16.155 cm By using the cosine rule, cosUAV = 13.416² + 15² - 16.155² 2(13.416)(15) UAV = 69º2’ 15 cm U 13.416 cm A

9. Rumus SOH CAH TOA Sin = T H Kos = S H Tan = T S SayaTelahHafal KalauSayaHafal TentuTidak Susah

10. Prepared By, NurulHanisahHalbani AsnitaMapasisi SharmizaAdlinaJunaidi