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Worksheet: Determinants and Areas of Triangles

Q1:

Find the area of the triangle below using determinants.

  • A13 square units
  • B36 square units
  • C26 square units
  • D18 square units

Q2:

Find the area of the triangle 𝐴 𝐡 𝐢 with vertices 𝐴 ( 1 , 4 ) , 𝐡 ( βˆ’ 4 , 5 ) , and 𝐢 ( βˆ’ 4 , βˆ’ 5 ) .

Q3:

Use determinants to find the area of the triangle with vertices ( 0 , βˆ’ 1 ) , ( 0 , 2 ) , and ( 5 , 0 ) .

Q4:

Use determinants to work out the area of the triangle with vertices ( 2 , βˆ’ 2 ) , ( 4 , βˆ’ 2 ) , and ( 0 , 2 ) by viewing the triangle as half of a parallelogram.

Q5:

Consider the quadrilateral with vertices 𝐴 ( 1 , 3 ) , 𝐡 ( 4 , 2 ) , 𝐢 ( 4 . 5 , 5 ) , and 𝐷 ( 2 , 6 ) .

By breaking it into two triangles as shown, calculate the area of this quadrilateral using determinants.

Q6:

Consider the equation If triangle 𝐴 𝐡 𝐢 has an area of 38, what is the radius of its circumcircle?

  • A4
  • B8
  • C 1 2
  • D2
  • E 1 8

Q7:

Find the area of the triangle below using determinants.

  • A17 square units
  • B38 square units
  • C34 square units
  • D19 square units

Q8:

Find the area of the triangle below using determinants.

  • A22 square units
  • B32 square units
  • C44 square units
  • D16 square units

Q9:

Find the area of the triangle below using determinants.

  • A13 square units
  • B30 square units
  • C26 square units
  • D15 square units

Q10:

Find the area of the triangle below using determinants.

  • A30 square units
  • B40 square units
  • C60 square units
  • D20 square units

Q11:

Find the area of the triangle below using determinants.

  • A3 square units
  • B36 square units
  • C6 square units
  • D18 square units

Q12:

Find the area of the triangle below using determinants.

  • A8 square units
  • B22 square units
  • C16 square units
  • D11 square units

Q13:

Find the area of the triangle below using determinants.

  • A10 square units
  • B34 square units
  • C20 square units
  • D17 square units

Q14:

Find the area of the triangle 𝐴 𝐡 𝐢 with vertices 𝐴 ( 1 , βˆ’ 5 ) , 𝐡 ( βˆ’ 4 , βˆ’ 2 ) , and 𝐢 ( 5 , βˆ’ 5 ) .