**Area of triangle worksheets :**

Here we are going to see some practice questions based on the topic area of triangle.

(1) Find the area of triangle whose vertices are (6,7) (2,-9) and (-4,1).

(2) Find the area of triangle whose vertices are (3,4) (2,-1) and (4,-6).

(3) Find the area of triangle whose vertices are (5,6) (2,4) and (1,-3).

(4) Find the area of triangle whose vertices are (1,3) (-7,6) and (5,-1).

(5) Find the area of triangle whose vertices are (1,1) (3,4) and (5,-2).

(6) Find the area of triangle whose vertices are (-3,-9) (-1,6) and (3,9).

(7) Find the area of triangle whose vertices are (-3,-9) (3,9) and (5,-8).

(8) Find the area of triangle whose vertices are (4,5) (4,2) and (-2,2).

(9) Find the area of triangle whose vertices are (3,1) (2,2) and (2,0).

(10) Find the area of triangle whose vertices are (3,1) (0,4) and (-3,1).

**Question 1 : **

Find the area of triangle whose vertices are (6,7) (2,-9) and (-4,1).

**Solution :**

Now we have to take anticlockwise direction. So, we have to take the points in the order A (6,7) C (-4,1) and B (2,-9)

x₁ = 6 x₂ = -4 x₃ = 2

y₁ = 7 y₂ = 1 y₃ = -9

Area of the triangle ACB

= (1/2) {(6 + 36 + 14) - (-28 + 2 - 54)}

= (1/2) {56 - ( -82 + 2)}

= (1/2) {56 - (-80) }

= (1/2) {56 + 80)}

= (1/2) x 136

= 68 Square units.

Hence, the area of ACB = 68 square units.

**Question 2 :**

Find the area of triangle whose vertices are (3,4) (2,-1) and (4,-6).

**Solution :**

Now we have to take anticlockwise direction. So, we have to take the points in the order A (6,7) C (-4,1) and B (2,-9)

x₁ = 3 x₂ = 2 x₃ = 4

y₁ = 4 y₂ = -1 y₃ = -6

Area of the triangle ACB

= (1/2) {(-3 - 12 + 16) - (8 - 4 - 18)}

= (1/2) {(-15 + 16) - (8 - 22)}

= (1/2) {1 - (-14) }

= (1/2) x (1 + 14)

= (1/2) x 15

= 15/2 = 7.5 Square units.

Hence, the area of ABC = 7.5 square units.

**Question 3 :**

Find the area of triangle whose vertices are (5,6) (2,4) and (1,-3).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order A (5,6) B (2,4) and C (1,-3)

x₁ = 5 x₂ = 2 x₃ = 1

y₁ = 6 y₂ = 4 y₃ = -3

Area of the triangle ABC

= (1/2) {(20 - 6 + 6) - (12 + 4 - 15)}

= (1/2) {20 - (16 - 15)}

= (1/2) {20 - (1) }

= (1/2) {20 - 1}

= (1/2) x 19

= 19/2 ==> 9.5 Square units.

Hence, the area of ABC = 9.5 square units.

**Question 4 : **

Find the area of triangle whose vertices are (1,3) (-7,6) and (5,-1).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order A (1,3) B (-7,6) and C (5,-1)

x₁ = 1 x₂ = -7 x₃ = 5

y₁ = 3 y₂ = 6 y₃ = -1

Area of the triangle ACB

= (1/2) {(6 + 7 + 15) - (-21 + 30 - 1)}

= (1/2) {28 - ( -22 + 30)}

= (1/2) {28 - (8) }

= (1/2) {28 - 8}

= (1/2) x 20

= 10 Square units.

Hence, the area of ABC = 10 square units.

**Question 5 :**

Find the area of triangle whose vertices are (1,1) (3,4) and (5,-2).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order B (3,3) A (1, 1) and C (5,-2)

x₁ = 3 x₂ = 1 x₃ = 5

y₁ = 3 y₂ = 1 y₃ = -2

Area of the triangle BAC

= (1/2) {(4 - 6 + 5) - (3 + 20 - 2)}

= (1/2) {(9 - 6) - (23 - 2)}

= (1/2) {3 - 21}

= (1/2) {-18}

= -18/2

= 9 Square units.

Hence, the area of ABC = 9 square units.

**Question 6 :**

Find the area of triangle whose vertices are (-3,-9) (-1,6) and (3,9).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order C (3,9) B (-1,6) and A (-3,-9)

Area of the triangle CBA

= (1/2) {(18 + 9 - 18) - (-9 - 18 - 27)}

= (1/2) {9 - ( -54)}

= (1/2) {9 + 54}

= (1/2) (63)

= (63/2)

= 31.5 Square units.

Hence, the area of CBA = 31.5 square units.

Let us see the solution of next problem on "Area of triangle worksheets".

**Question 7 :**

Find the area of triangle whose vertices are (-3,-9) (3,9) and (5,-8).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order B (3,9) A (-3,-9) and C (5,-8)

x₁ = 3 x₂ = -3 x₃ = 5

y₁ = 9 y₂ = -9 y₃ = -8

Area of the triangle BAC

= (1/2) {(-27 - 24 + 45) - (-27 - 45 - 24)}

= (1/2) {(-51 + 45) - (-96)}

= (1/2) {-6 + 96}

= (1/2) (90)

= (90/2)

= 45 Square units.

Hence, the area of BAC = 45 square units.

Let us see the solution of next problem on "Area of triangle worksheets".

**Question 8 :**

Find the area of triangle whose vertices are (4,5) (4,2) and (-2,2).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order A (4,5) C (-2,2) and B (4,2)

x₁ = 4 x₂ = -2 x₃ = 4

y₁ = 5 y₂ = 2 y₃ = 2

Area of the triangle ACB

= (1/2) {(8 - 4 + 20) - (-10 + 8 + 8)}

= (1/2) {(28 - 4) - ( -10 + 16)}

= (1/2) (24 - 6)

= (1/2) x 18

= (18/2)

= 9 Square units.

Hence, the area of ACB = 9 square units.

Let us see the solution of next problem on "Area of triangle worksheets".

**Question 9 :**

Find the area of triangle whose vertices are (3,1) (2,2) and (2,0).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order B (2,2) C (2,0) and A (3,1)

x₁ = 2 x₂ = 2 x₃ = 3

y₁ = 2 y₂ = 0 y₃ = 1

Area of the triangle BCA

= (1/2) {(0 + 2 + 6) - (4 + 0 + 2)}

= (1/2) {8 - 6}

= (1/2) (2)

= (2/2)

= 1 Square units.

Hence, the area of ACB = 1 square units.

Let us see the solution of next problem on "Area of triangle worksheets".

**Question 10 :**

Find the area of triangle whose vertices are (3,1) (0,4) and (-3,1).

**Solution :**

Now we have to take anticlockwise direction. So we have to take the points in the order B (0,4) C (-3,1) and A (3,1)

x₁ = 0 x₂ = -3 x₃ = 3

y₁ = 4 y₂ = 1 y₃ = 1

Area of the triangle BCA

= (1/2) {(0 -3 + 12) - (-12 + 3 + 0)}

= (1/2) {9 - ( -12 + 3)}

= (1/2) {9 - (-9) }

= (1/2) {9 + 9)}

= (1/2) x 18

= 9 Square units.

Hence, the area of BCA = 9 square units.

**Related Topics**

- Section formula
- Area of triangle
- Area of quadrilateral
- Centroid
- Centroid of the triangle worksheets
- Finding missing vertex using centroid worksheet
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- 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
- Point of intersection Worksheets
- concurrency of straight line
- Concurrency of straight lines worksheet
- Circumcentre of a triangle
- Circumcentre of Triangle Worksheet
- Orthocentre of a triangle
- Orthocentre of Triangle Worksheet
- 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
- Parabola
- Ellipse

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