find the area of equator triangle whose a parameter is is 45
Answers
Question:
Find the area of an equilateral triangle whose perimeter is 45 cm.
Answer:
The area of the equilateral triangle is 56.25 √3 cm².
Step-by-step-explanation:
We have given the perimeter of an equilateral triangle as 45 cm.
We have to find the area of the triangle.
Now, we know that,
Perimeter of triangle = Sum of all sides
⇒ Perimeter of equilateral triangle = 3 × Side
⇒ 45 = 3 × Side
⇒ Side = 45 ÷ 3
⇒ Side = 15 cm
Now, we know that,
Area of equilateral triangle = ( √3 / 4 ) × ( side )²
⇒ A ( Equilateral △ ) = ( √3 / 4 ) × ( 15 )²
⇒ A ( Equilateral △ ) = ( √3 / 4 ) × 15 × 15
⇒ A ( Equilateral △ ) = √3 × 15 × 15 ÷ 4
⇒ A ( Equilateral △ ) = 15 √3 × 15 ÷ 4
⇒ A ( Equilateral △ ) = 15 √3 × 3.75
⇒ A ( Equilateral △ ) = 56.25 √3 cm²
∴ The area of the equilateral triangle is 56.25 √3 cm².
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Additional Information:
1. Triangle:
A geometric figure formed by binding three segments and having three corners is called a traingle.
2. Types of triangle:
A. Based on angles
B. Based on sides
3. Based on angles:
A. Acute angled triangle ( < 90° )
B. Right angled triangle ( 90° )
C. Obtuse angled triangle ( > 90° )
4. Based on sides:
A. Equilateral triangle
All sides are equal.
B. Isosceles triangle
Two sides are equal.
C. Scalene triangle
No side is of equal measures.
5. Equilateral triangle:
1. A triangle with all sides equal is called as an equilateral triangle.
2. The measure of an angle of an equilateral triangle is 60°.
3. An altitude drawn from a vertex of an equilateral triangle to the opposite side is the altitude, perpendicular bisector and the angle bisector.
6. Perimeter of equilateral triangle:
The sum of all sides of equilateral triangle is its perimeter.
Formula:
Perimeter of equilateral triangle = 3 × Side
7. Area of equilateral triangle:
The part occupied by the sides of an equilateral triangle is its area.
Formula:
Area of equilateral triangle = ( √3 / 4 ) × ( Side )²
Answer:
Question:
Find the area of an equilateral triangle whose perimeter is 45 cm.
Answer:
The area of the equilateral triangle is 56.25 √3 cm².
Step-by-step-explanation:
We have given the perimeter of an equilateral triangle as 45 cm.
We have to find the area of the triangle.
Now, we know that,
Perimeter of triangle = Sum of all sides
⇒ Perimeter of equilateral triangle = 3 × Side
⇒ 45 = 3 × Side
⇒ Side = 45 ÷ 3
⇒ Side = 15 cm
Now, we know that,
Area of equilateral triangle = ( √3 / 4 ) × ( side )²
⇒ A ( Equilateral △ ) = ( √3 / 4 ) × ( 15 )²
⇒ A ( Equilateral △ ) = ( √3 / 4 ) × 15 × 15
⇒ A ( Equilateral △ ) = √3 × 15 × 15 ÷ 4
⇒ A ( Equilateral △ ) = 15 √3 × 15 ÷ 4
⇒ A ( Equilateral △ ) = 15 √3 × 3.75
⇒ A ( Equilateral △ ) = 56.25 √3 cm²
∴ The area of the equilateral triangle is 56.25 √3 cm².
─────────────────────
Additional Information:
1. Triangle:
A geometric figure formed by binding three segments and having three corners is called a traingle.
2. Types of triangle:
A. Based on angles
B. Based on sides
3. Based on angles:
A. Acute angled triangle ( < 90° )
B. Right angled triangle ( 90° )
C. Obtuse angled triangle ( > 90° )
4. Based on sides:
A. Equilateral triangle
All sides are equal.
B. Isosceles triangle
Two sides are equal.
C. Scalene triangle
No side is of equal measures.
5. Equilateral triangle:
1. A triangle with all sides equal is called as an equilateral triangle.
2. The measure of an angle of an equilateral triangle is 60°.
3. An altitude drawn from a vertex of an equilateral triangle to the opposite side is the altitude, perpendicular bisector and the angle bisector.
6. Perimeter of equilateral triangle:
The sum of all sides of equilateral triangle is its perimeter.
Formula:
Perimeter of equilateral triangle = 3 × Side
7. Area of equilateral triangle:
The part occupied by the sides of an equilateral triangle is its area.
Formula:
Area of equilateral triangle = ( √3 / 4 ) × ( Side )²
Step-by-step explanation:
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