Question

In ∆ ABC, AC = 8 cm, BC = 4 cm and AE = 5 cm. 

Find 

(i) the area of the AABC 

(ii) BD.

Answer 1

(i) In ∆ ABC, Base (BC) = 4 cm, 

Height (AE) = 5 cm.

Area of the ∆ ABC = \(\frac {1}2\) × base × height

= \(\frac {1}2\) × 4 × 5 = 10 sq.cm.

(ii) In ABAC, Base (AC) = 8 cm, 

height (BD) = ?, 

Area of ∆ BAC = 10 sq.cm 

Area of the ∆ BAC = \(\frac {1}2\) × base × height

i. e. 10 = \(\frac {1}2\) × 8 × BD

BD = 10 × \(\frac {2}8\) = \(\frac {10}4\) = \(\frac {5}2\) = 2.5

So, height (BD) = 2.5 cm