In this worksheet, we will practice finding the side lengths, perimeter, and area of a triangle on the coordinate plane using the Pythagorean theorem.

**Q1: **

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.

**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.

**Q3: **

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

**Q4: **

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

**Q5: **

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 .

**Q6: **

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

**Q7: **

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 .

**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: **

Find the area of the following right-angled triangle.

**Q10: **

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

**Q11: **

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

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

**Q12: **

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

**Q13: **

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

**Q14: **

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

**Q15: **

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

- A ,
- B ,
- C ,
- D ,
- E ,

**Q16: **

Find the area of the coloured region.

- A100
- B70
- C85
- D40
- E60

**Q17: **

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

**Q18: **

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

**Q19: **

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

**Q20: **

Find the area of the following right-angled triangle.

**Q21: **

Find the area of the following right-angled triangle.