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Worksheet: Side Lengths, Perimeter, and Area of a Triangle

Q1:

Find the area of the colored region.

Q2:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( 2 , βˆ’ 2 ) , ( 4 , βˆ’ 2 ) , and ( 0 , 2 ) respectively.

Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution to two decimal places.

Work out the area of the triangle 𝐴 𝐡 𝐢 .

Q3:

The quadrilateral 𝐴 𝐡 𝐢 𝐷 is formed by the points 𝐴 ( 1 5 , 7 ) , 𝐡 ( 1 3 , 3 ) , 𝐢 ( 5 , 3 ) , and 𝐷 ( 7 , 7 ) . Calculate the length of 𝐡 𝐢 .

Q4:

Given that the vertices of β–³ 𝑃 𝑄 𝑅 are 𝑃 ( 0 , 3 ) , 𝑄 ( βˆ’ 1 , βˆ’ 4 ) , and 𝑅 ( 3 , βˆ’ 4 ) , determine its perimeter, rounded to the nearest tenth, and then find its area.

  • Aperimeter = 1 2 , area = 1 4
  • Bperimeter = 1 8 . 7 , area = 2 8
  • Cperimeter = 1 2 , area = 2 8
  • Dperimeter = 1 8 . 7 , area = 1 4
  • Eperimeter = 1 8 . 1 , area = 2 4 . 7 5

Q5:

Given that the vertices of β–³ 𝑃 𝑄 𝑅 are 𝑃 ( βˆ’ 2 , 7 ) , 𝑄 ( βˆ’ 6 , 4 ) , and 𝑅 ( 3 , 4 ) , determine its perimeter, rounded to the nearest tenth, and then find its area.

  • Aperimeter = 2 7 , area = 1 3 . 5
  • Bperimeter = 1 9 . 8 , area = 2 7
  • Cperimeter = 2 7 , area = 2 7
  • Dperimeter = 1 9 . 8 , area = 1 3 . 5
  • Eperimeter = 1 9 , area = 7 . 5

Q6:

Given that the coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( βˆ’ 2 , 1 ) , ( βˆ’ 2 , βˆ’ 8 ) , and ( 9 , βˆ’ 8 ) , respectively, determine the area of β–³ 𝐴 𝐡 𝐢 .

  • A11square units
  • B99square units
  • C9square units
  • D49.5square units

Q7:

Given that the coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( βˆ’ 5 , 4 ) , ( βˆ’ 5 , βˆ’ 5 ) , and ( 6 , βˆ’ 5 ) , respectively, determine the area of β–³ 𝐴 𝐡 𝐢 .

  • A27.5square units
  • B99square units
  • C22.5square units
  • D49.5square units

Q8:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( 0 , 5 ) , ( 1 , βˆ’ 2 ) , and ( βˆ’ 2 , βˆ’ 2 ) respectively.

Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution to two decimal places.

Work out the area of the triangle 𝐴 𝐡 𝐢 .

Q9:

The vertices of quadrilateral 𝑃 𝑄 𝑅 𝑆 are 𝑃 ( 2 , 7 ) , 𝑄 ( 8 , 7 ) , 𝑅 ( 8 , βˆ’ 3 ) , and 𝑆 ( 2 , βˆ’ 3 ) . Find the lengths of 𝑃 𝑄 and 𝑄 𝑅 .

  • A 𝑃 𝑄 = 1 2 , 𝑄 𝑅 = 2 0
  • B 𝑃 𝑄 = 1 0 , 𝑄 𝑅 = 6
  • C 𝑃 𝑄 = 7 , 𝑄 𝑅 = 5
  • D 𝑃 𝑄 = 6 , 𝑄 𝑅 = 1 0
  • E 𝑃 𝑄 = 5 , 𝑄 𝑅 = 7

Q10:

A triangle is drawn in the coordinate plane with its vertices at 𝐴 ( 2 , 2 ) , 𝐡 ( 7 , 2 ) , and 𝐢 ( 4 . 5 , 7 ) .

Find the length of the base 𝐴 𝐡 .

Find the height of the triangle.

Hence, find the area of the triangle.

  • A22.5 square units
  • B25 square units
  • C12.5 square units
  • D6.25 square units
  • E10 square units

Q11:

Find the area of the triangle 𝐴 𝐡 𝐢 given the line drawn from the point 𝐴 ( βˆ’ 2 , 8 ) is perpendicular to the straight line passing through the points 𝐡 ( 4 , βˆ’ 7 ) and 𝐢 ( 1 0 , βˆ’ 9 ) . Give the answer to the nearest square unit.

  • A22 square unit
  • B19 square unit
  • C78 square unit
  • D39 square unit

Q12:

In the figure, the coordinates of points , , and are , , and , respectively. Determine the lengths of and , and then calculate the area of , where a unit length .

  • A , , area of
  • B , , area of
  • C , , area of
  • D , , area of

Q13:

Given that 𝐴 𝐡 𝐢 is an isosceles triangle, where the coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( 8 , βˆ’ 2 ) , ( βˆ’ 2 , βˆ’ 2 ) , and ( 0 , βˆ’ 8 ) , find the area of β–³ 𝐴 𝐡 𝐢 .

Q14:

Given that 𝐴 𝐡 𝐢 is an isosceles triangle, where the coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( 8 , 5 ) , ( 0 , 4 ) , and ( 0 , 6 ) , find the area of β–³ 𝐴 𝐡 𝐢 .

Q15:

Find the area of the following right triangle.

  • A
  • B32
  • C116
  • D29

Q16:

Find the area of the following right triangle.

  • A
  • B57
  • C204
  • D51

Q17:

Find the area of the following right triangle.

  • A
  • B22
  • C80
  • D20

Q18:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( βˆ’ 2 , βˆ’ 2 ) , ( βˆ’ 1 , 7 ) , and ( 3 , 1 ) respectively. Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution to two decimal places.

Q19:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( 0 , βˆ’ 1 ) , ( 0 , 2 ) , and ( 5 , 0 ) respectively. Work out the area of the triangle 𝐴 𝐡 𝐢 .

Q20:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( 2 , βˆ’ 1 ) , ( 3 , 3 ) , and ( 6 , 1 ) respectively.

Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution to one decimal place.

By drawing a rectangle through the vertices of the triangle, or otherwise. Work out the area of the triangle 𝐴 𝐡 𝐢 .

Q21:

A triangle has vertices at the points 𝐴 , 𝐡 , and 𝐢 with coordinates ( 3 , 3 ) , ( βˆ’ 1 , 3 ) , and ( 7 , βˆ’ 6 ) respectively. Work out the perimeter of the triangle 𝐴 𝐡 𝐢 . Give your solution to two decimal places.