Grade 10 Maths · Analytical Geometry

Calculate area or perimeter

Choose the right formula and find the area or perimeter of a shape (for example a circle with radius 3 has area π × 3² ≈ 28,27).

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Area and Perimeter Grade 9: Square, rhombus, parallelogram, rectangleKevinmathscience

Area and Perimeter: CirclesKevinmathscience

Area and Perimeter Grade 9: TriangleKevinmathscience

Finding the Area of a Composite Figure | Area of Composite RectanglesMath with Mr. J

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Question 3.6 · May/June 2025 · Paper 2 · National (DBE) · 5 marks

In the diagram below,

Δ SRT

is drawn where R lies on the x-axis and S lies to the left of R. T lies on the y-axis and the coordinates of S are

(m; 1)

.

The equation of RT is

2 x - y + 10 = 0

3.6 If

R^{'}

is the reflection of R about the line

x = 0

, calculate the area of

R V T R^{'}

.(5)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate area or perimeter

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3. Question 5.4 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
In the diagram, the graphs of $f (x) = lo g_{a} x$ and $g$ are drawn. Graph $g$ is the reflection of $f$ in the line $y = x$ . Graph $f$ passes through the point P $(4; 2)$ . Q is the $x$ -intercept of $f$ and R is the $y$ -intercept of $g$ .
5.4 T is a point on $f$ in the first quadrant where TR is parallel to the $x$ -axis. Calculate the area of $△$ RTP $^{'}$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  x-coordinate of T $1 = lo g_{2} x ⟹ x = 2$ , so $T (2; 1)$
  1 mark · Convert between log and exponential form
2. ✓
  Length RT $RT = 2$ units
  1 mark · Find a horizontal or vertical length
3. ✓
  Length P'T $P^{'} T = 3$ units
  1 mark · Find a horizontal or vertical length
4. ✓
  Calculate areaArea $△ RT P^{'} = \frac{1}{2} \times 2 \times 3 = 3$ units $^{2}$
  1 mark · Calculate area or perimeter
4. Question 3.2 · November 2024 · Paper 1 · National (DBE) · 4 marks
A circle with radius $6$ cm is drawn. A second, smaller circle is drawn through the centre of the first circle and also touches the first circle internally, as shown in the diagram. A third, smaller circle is drawn through the centre of the second circle and touches the second circle internally. The process of drawing circles continues and forms a geometric pattern.
3.2 Calculate the sum of the areas of the first 10 circles.(4)
Show the memo (4 ticks)Memo
1. ✓
  Identify the series of areasAreas: $π (6)^{2}; π (3)^{2}; π (\frac{3}{2})^{2}; ...$
  Series: $36 π; 9 π; \frac{9}{4} π; ...$
  1 mark · Calculate area or perimeter
2. ✓
  Identify geometric parameters $a = 36 π$
  $r = \frac{1}{4}$
  1 mark · Find the common ratio
3. ✓
  Substitute into sum formula $S_{10} = \frac{36 π (( \frac{1}{4} ) ^{10} - 1 )}{\frac{1}{4} - 1}$
  1 mark · Calculate a geometric series sum
4. ✓
  Calculate final answer $S_{10} = 150, 80$
  1 mark · Calculate a geometric series sum
5. Question 4.2.1 · March 2021 · Provincial · 3 marks
4.2 In the diagram below, square ACDE has an area of $256 c m^{2}$ and $A B = BC$ .
4.2.1 Determine the length of AC. (Let $A C = x$ )(3)
Show the memo (3 ticks)Memo
1. ✓
  Area of a square (S)Area of square $= A C \times A E$ and $A C = A E = x$
  1 mark · Calculate area or perimeter
2. ✓
  $x^{2} = 256$ $x^{2} = 256$ cm $^{2}$
  1 mark · Calculate area or perimeter
3. ✓
  Answer $x = 16$ cm
  1 mark · Calculate area or perimeter
6. Question 3.4 · November 2024 · Paper 2 · Provincial · 4 marks
In the figure, $Δ A BC$ has vertices $A (- 11; 2)$ , $B (3; - 5)$ and $C (6; 1)$ .
3.4 Calculate the area of $Δ A BC$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Length of AB $A B = (3 - (- 11))^{2} + (- 5 - 2)^{2}$
  $A B = 1 4^{2} + (- 7)^{2} = 196 + 49 = 245 = 75$
  1 mark · Calculate distance between two points
2. ✓
  Area formulaArea $= \frac{1}{2} \times A B \times BC$ (since $A \hat{B} C = 9 0^{\circ}$ )
  1 mark · Calculate area or perimeter
3. ✓
  Substitution $= \frac{1}{2} \times 75 \times 35$
  1 mark · Calculate area or perimeter
4. ✓
  Answer $= \frac{105}{2} = 52, 5$ units $^{2}$
  1 mark · Calculate area or perimeter

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