Answer:
6.0square units
Step-by-step explanation:
Area of a triangle = 1/2 × base × height
The height of the given triangle is CD and the base is AB
To get the height CD, we need to use the Pythagoras theorem on the triangle ACD
AC² = CD² + AD²
CD² = 3²-1.8²
CD² = 5.76
CD = √5.76
CD = 2.4
According to ∆ABC,
AB² = AC²+BC²
Since AB = AD+DB then;
(AD+DB)² = AC²+BC²
AD² + 2(AD)(DB)+DB² = AC²+BC²
DB² = AC²+BC² - AD² - 2(AD)(DB)... 1
According to ∆BCD
BC² = CD²+DB²
DB² = BC²-CD²...2
Equating 1 and 2
AC²+BC² - AD² - 2(AD)(DB) = BC²-CD²
AC² - AD² - 2(AD)(DB) + CD² = 0
AC = 3
AD = 1.8
CD = 2.4
On substituting
3²-1.8² - 2(1.8)DB +2.4² = 0
9-3.24-3.6DB+5.76 = 0
11.52 - 3.6DB = 0
3.6DB = 11.52
DB = 11.52/3.6
DB = 3.2
The base of the triangle
AB = AD+DB
AB = 1.8+3.2
AB = 5.0
Area of the triangle = 1/2 × 2.4 × 5
= 1.2 × 5
= 6.0square units
