First steps in coordinates · Ages 12–13
Areas on the coordinate plane
Split and add, or a rectangle round it minus the corners.
How to do it
Method
Split and add, or a rectangle round it minus the corners
Base 5, height 5: 12 × 5 × 5 = 12.5
Another way
Rectangle minus corners
6 × 5 − 9 − 4 − 5 = 12
In full
First find the lengths of the horizontal and vertical sides from the coordinates, then use the area formulas. One way: split the shape into rectangles and right triangles, work out each and add. Another: draw a rectangle round it with sides parallel to the axes, and take away the right triangles left over at its corners. Triangle A(−2, −1), B(3, −1), C(1, 4): the base AB = 3 − (−2) = 5, the height from C to AB is 4 − (−1) = 5, so the area is 12 × 5 × 5 = 12.5. A triangle with no horizontal or vertical side is easiest with the rectangle round it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Triangle ABC has corners A(−3, −3), B(4, −3) and C(0, −5). Base AB = , height = , area = square units.
Fill in each blank
Show the answer and working
Answer: 7, 2, 7
AB is horizontal, so the base is the gap in x, 7; the height is the gap in y from C to AB, 2; 12 × 7 × 2 = 7.
Example 2
Triangle ABC has corners A(−5, −6), B(−5, 1) and C(−3, 0). Its area is square units.
Show the answer and working
Answer: 7
AB is vertical, so take it as the base: AB = 7; the height is C's distance across to AB, 2; area = 12 × 7 × 2 = 7.
Example 3
What is the area of triangle ABC, in square units?
- A. 31.5
- B. 3.5
- C. 63
- D. 27
Choose the right answer
Show the answer and working
Answer: A. 31.5
AB is horizontal: base = 4 − (−5) = 9, height = C's distance to AB, 7, area = 12 × 9 × 7 = 31.5.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Rectangle ABCD has corners A(−4, −5), B(4, −5), C(4, 2) and D(−4, 2). Its area is square units.
Answer:
2.Triangle ABC has corners A(−3, 2), B(2, 2) and C(−5, −4). Its area is square units.
Answer:
3.Triangle ABC has corners A(−2, −1), B(−2, 6) and C(−1, −5). Its area is square units.
Answer:
4.What is the area of triangle ABC, in square units?
- A. 15
- B. 7.5
- C. 1.5
- D. 12.5
Choose the right answer
Answer:
5.Trapezium ABCD has corners A(−6, −1), B(1, −1), C(2, 1) and D(−4, 1). Its area is square units.
Answer:
All the answers
- 1. 56
- 2. 15
- 3. 3.5
- 4. B. 7.5
- 5. 13
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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