find the area of triangle ABC from given figure
Answers
Answer:
Step-by-step explanation:
Given:
From the figure we have,
∠D = 90°
BC = 16 cm
CD = 12 cm
AC = 13 cm
To find:
The area of the Δ ABC
Solution:
Formulas to be used:
- Area of triangle = ½ × base × height
- Pythagoras theorem of a right angled triangle: Hypotenuse² = Perpendicular² + Base²
From the figure given in the question,
Considering Δ ACD, we have
Hypotenuse, AC = 13 cm
Base, CD = 12 cm
Perpendicular AD needs to be calculated
So, using the formula of Pythagoras theorem, we get
AC² = AD² + CD²
⇒ 13² = AD² + 12²
⇒ AD² = 13² - 12²
⇒ AD² = 169 - 144
⇒ AD² = 25
⇒ AD = √25
⇒ AD = 5 cm
Now,
Finding the area of Δ ACD
Base, CD = 12 cm
Height, AD = 5 cm
Using the formula of area of triangle, we get
Area of Δ ACD = ½ × 12 × 5 = 6 × 5 = 30 cm ..... (i)
Finding the area of Δ ABD
Base, BD = BC + CD = 16 + 12 = 28 cm
Height, AD = 5 cm
Using the formula of area of triangle, we get
Area of Δ ABD = ½ × 28 × 5 = 14 × 5 = 70 cm ..... (ii)
Finding the area of Δ ABC
In order to find the area of Δ ABC we will subtract the area of Δ ACD from the area of Δ ABD as calculated in equations (i) & (ii).
So,
The area of Δ ABC is given by,
= [ Area (Δ ABD) ] - [ Area (Δ ACD) ]
= [ 70 cm ] - [ 30 cm ]
= 40 cm
Thus, the area of Δ ABC from the given figure is 40 cm.
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