AB = 9 cm AC = 9cm BC = 10cm
(a) Calculate the area, in cm2
to one decimal place, of triangle ABC.
Answers
Answer:
Given:
AB = 9 cm, AC = 9 cm, BC = 10 cm
To Find:
Area of ∆ ABC
Solution:
So, we will draw a perpendicularly line from the vertex A of ∆ ABC, namely AM.
Since, AB = AC, AM will divide BC into 2 equal parts, i.e., BM = CM.
→ BM = CM = BC/2 = 10/2 cm
→ BM = CM = 5 cm
So, in ∆ ABM,
AB = 9 cm, BM = 5 cm
Using Pythagoras Theorem,
AB² = AM² + BM²
9² = AM² + 5²
81 = AM² + 25
AM² = 81 - 25
AM² = 56
AM = cm
AM = 7.48 cm
Therefore, height (h) = AM = 7.48 cm
and, base (b) = BC = 10 cm
Area of ∆ ABC =
Hence, Area of ABC is 37.4 cm².
Step-by-step explanation:
Answer:
Area of of triangle ABC = 37.4 cm^2
Step-by-step explanation:
Area of triangle is 1/2 bh
Now we know base(b) BC is 10 cm
we have to find the height (h)
if we take middle point of BC is D then BD=5 cm
using Pythagorean theorem
height (AD) = Sq.root of AB^2 - BD^2
= 9^2 - 5^2
= 81-25
=sq.root of 56
height (h) = 7.48 cm
if we substitute values
Area of triangle = 1/2× bh
=1/2×10×7.48
=1/2×74.8
Area of triangle =37.4 cm^2