# 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 , , and with coordinates , , and respectively.

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

Work out the area of the triangle .

Q3:

The quadrilateral is formed by the points , , , and . Calculate the length of .

Q4:

Given that the vertices of are , , and , determine its perimeter, rounded to the nearest tenth, and then find its area.

• Aperimeter , area
• Bperimeter , area
• Cperimeter , area
• Dperimeter , area
• Eperimeter , area

Q5:

Given that the vertices of are , , and , determine its perimeter, rounded to the nearest tenth, and then find its area.

• Aperimeter , area
• Bperimeter , area
• Cperimeter , area
• Dperimeter , area
• Eperimeter , area

Q6:

Given that the coordinates of the points ,, and are , , and , respectively, determine the area of .

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

Q7:

Given that the coordinates of the points ,, and are , , and , respectively, determine the area of .

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

Q8:

A triangle has vertices at the points , , and with coordinates , , and respectively.

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

Work out the area of the triangle .

Q9:

The vertices of quadrilateral are , , , and . Find the lengths of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q10:

A triangle is drawn in the coordinate plane with its vertices at , , and .

Find the length of the base .

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 given the line drawn from the point is perpendicular to the straight line passing through the points and . 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 is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

Q14:

Given that is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

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 , , and with coordinates , , and respectively. Work out the perimeter of the triangle . Give your solution to two decimal places.

Q19:

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the area of the triangle .

Q20:

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . 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 .

Q21:

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the perimeter of the triangle . Give your solution to two decimal places.