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Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?
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Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the hei...
Area of Triangle ABC
To find the area of triangle ABC, we can use the formula for the area of a triangle:
- Area = (1/2) × base × height
In this case:
- Base (BC) = 9 cm
- Height (AD) = 6 cm
Calculating the area:
- Area = (1/2) × 9 cm × 6 cm
- Area = 27 cm²
Thus, the area of triangle ABC is 27 cm².
Height from C to Line AE
To find the height from point C to line AE (denote this height as CE), we can analyze the triangle further.
1. Coordinates Setup:
- Place point A at (0, 6).
- Point B will be at (-4.5, 0) and point C at (4.5, 0) since it is isosceles and symmetrical.
2. Finding Line AE:
- The line AE will be the base (BC) where the coordinates of points B and C are (-4.5, 0) and (4.5, 0) respectively.
3. Using Distance Formula:
- The distance from point C (4.5, 0) to line AE (y = 0) is simply the y-coordinate of point C since line AE lies on y=0.
- Therefore, height CE = 0 - 0 = 0 cm.
The height from point C to line AE is 0 cm, as point C lies directly on line AE.
Summary
- Area of Triangle ABC: 27 cm²
- Height from C to line AE (CE): 0 cm
This analysis helps understand the geometric properties of triangle ABC, reinforcing concepts of area and height in isosceles triangles.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
- Area = (1/2) × base × height
In this case:
- Base (BC) = 9 cm
- Height (AD) = 6 cm
Calculating the area:
- Area = (1/2) × 9 cm × 6 cm
- Area = 27 cm²
Thus, the area of triangle ABC is 27 cm².
Height from C to Line AE
To find the height from point C to line AE (denote this height as CE), we can analyze the triangle further.
1. Coordinates Setup:
- Place point A at (0, 6).
- Point B will be at (-4.5, 0) and point C at (4.5, 0) since it is isosceles and symmetrical.
2. Finding Line AE:
- The line AE will be the base (BC) where the coordinates of points B and C are (-4.5, 0) and (4.5, 0) respectively.
3. Using Distance Formula:
- The distance from point C (4.5, 0) to line AE (y = 0) is simply the y-coordinate of point C since line AE lies on y=0.
- Therefore, height CE = 0 - 0 = 0 cm.
The height from point C to line AE is 0 cm, as point C lies directly on line AE.
Summary
- Area of Triangle ABC: 27 cm²
- Height from C to line AE (CE): 0 cm
This analysis helps understand the geometric properties of triangle ABC, reinforcing concepts of area and height in isosceles triangles.
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Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?
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Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?.
Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Triangle ABC is isosceles with Ab = AC = 7.5 cm and BC= 9 cm . the height ad from a to BC is 6 CM . find the area of triangle ABC what will be the height from c to ..i...e..CE?.
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