**Triangle worksheet solution1 :**

Here we are going to see solution for each problems of the topic area of triangle worksheet.

(1) Find the are of the triangle formed by the points.

(i) (0, 0) (3, 0) and (0, 2)

**Solution:**

Let A (0, 0) , B(3, 0) and C (0, 2)are the vertices of the triangle taken in order.

x₁ = 0 x₂ = 3 x₃ = 0

y₁ = 0 y₂ = 0 y₃ = 2

Area of the triangle ABC

= (1/2) [ (0 + 6 + 0) – (0 + 0 + 0)]

= (1/2) [6 - 0]

= (1/2) [6]

= 3 square units

Hence, the area of ABC = 3 square units.

(ii) (5, 2) (3, -5) and (-5, -1)

**Solution:**

Let A (-5, -1) , B (3, -5) and C (5, 2) are the vertices of the triangle taken in order.

x₁ = -5 x₂ = 3 x₃ = 5

y₁ = -1 y₂ = -5 y₃ = 2

Area of the triangle ABC

= (1/2) [ (25 + 6 - 5) – (-3 - 25 - 10)]

= (1/2) [(31 - 5) –(-38)]

= (1/2) [26 +38]

= (1/2) [64]

= 32 square units

Hence, the area of ABC = 32 square units.

(iii) (-4, -5) (4, 5) and (-1, -6)

**Solution:**

Let A (-4, -5) , B (-1, -6) and C (4, 5) are the vertices of the triangle taken in order.

x₁ = -4 x₂ = -1 x₃ = 4

y₁ = -5 y₂ = -6 y₃ = 5

Area of the triangle ABC

= (1/2) [ (24 - 5 - 20) – (5 - 24 - 20)]

= (1/2) [(24 - 25) –(5 - 44)]

= (1/2) [(-1) – (-39)]

= (1/2) [-1 + 39]

= (1/2) [38]

= 19 square units

Hence, the area of ABC = 19 square units.

- Section formula
- Area of quadrilateral
- Centroid
- Midpoint
- Distance between two points
- Distance between two points worksheet
- Slope of the line
- Equation of the line
- Equation of line using two points worksheet
- Equation of the line using point and slope worksheets
- Point of intersection of two lines
- concurrency of straight line
- Circumcentre of a triangle
- Orthocentre of a triangle
- Incentre of a triangle
- Locus
- Perpendicular distance
- Angle between two straight lines
- Equation of a circle
- With center and radius
- With endpoints of a diameter
- Equation of a circle passing though three points
- Length of the tangent to a circle
- Equation of the tangent to a circle
- Family of circles
- Orthogonal circles

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