Question

Q.4)Find area of an isosceles traingle whose sides AB=AC=5cm and BC=8 cm.




Answer correctly

Answer 1

Answer:12 sq.cm

Step-by-step explanation:

For further details Refer to the pictures in attachment..

Answer 2

Your Answer:

Given:-

• Triangle ABC is an isosceles triangle, where AB = AC = 5cm
• BC = 8cm

To Find:-

• Area of Triangle

Solution:-

Draw a perpendicular AD on BC

So,

$\tt BD = DC ( \because a \ perpendicular \ divides \\\\ \qquad \ the \ base \ in \ two \ equal \ parts \ in \ an \ isosceles \ triangle )$

$\tt In \ \triangle ACD \\\\ \tt where, \\\\ \tt \star \angle ADC= 90^o \\\\ \tt \star AC = 5 \ and \ \ DC = BC/2 = 8/2 = 4cm$

Applying Pythagoras Theorem in this triangle

$\tt AC^2 = DC^2 + AD^2 \\\\ \tt \Rightarrow (5)^2 = (4)^2 + AD^2 \\\\ \tt \Rightarrow 25 = 16 + AD^2 \\\\ \tt \Rightarrow 9 = AD^2 \\\\ \tt \Rightarrow AD = 3cm$

Now,

$\tt Area \ of \ \triangle ABC = \dfrac{1}{2} \times base \times height \\\\ \tt \Rightarrow Area \ of \ \triangle ABC = \dfrac{1}{2} \times BC \times AD \\\\ \tt \Rightarrow Area \ of \ \triangle ABC = \dfrac{1}{2} \times 8 \times 3 \\\\ \tt \Rightarrow Area \ of \ \triangle ABC = 12cm^2$

So, Area of Triangle is 12cm^2