AREA OF TRIANGLE WORKSHEETS

About "Area of triangle worksheets"

Area of triangle worksheets :

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

Area of triangle worksheets - Practice questions

(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).

Area of triangle worksheets - Solution

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
• 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
• 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

After having gone through the stuff given above, we hope that the students would have understood "Area of triangle worksheets"

Apart from the stuff given above, if you want to know more about "Area of triangle worksheets", please click here.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6