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.
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