Areas of circles, sectors and composite shapes

Area formulas for rectangles, triangles, parallelograms, trapeziums, rhombuses, circles and sectors, and areas of composite shapes by adding and subtracting.

Formulas

Triangle: $\tfrac{1}{2}bh$
Parallelogram: $bh$
Trapezium: $\tfrac{1}{2}(a + b)h$

Rhombus or kite: $\tfrac{1}{2}xy$ (diagonals)
Circle: $\pi r^2$
Sector: $\dfrac{\theta}{360} \times \pi r^2$

Example 1●●

Find the area of a sector with radius $6$ and angle $90^\circ$.

$\dfrac{90}{360} \times \pi \times 36 = 9\pi \approx 28.27$

Example 2●●●

Find the area of the ring (annulus) between circles of radius $5$ and $3$.

$\pi(5^2) - \pi(3^2) = 25\pi - 9\pi = 16\pi$

$\approx 50.27$ square units

Flashcards

Trapezium

$\tfrac{1}{2}(a + b)h$

Sector area

$\dfrac{\theta}{360}\pi r^2$

Annulus

$\pi(R^2 - r^2)$

Practice

Area of a sector: radius $6$, angle $90^\circ$ (2 d.p.)?
Area between circles of radius $5$ and $3$ (2 d.p.)?
Trapezium with parallel sides $5$ and $9$, height $4$. Area?
Rhombus with diagonals $6$ and $8$. Area?
Area of a circle with radius $4$ (2 d.p.)?
Area of a semicircle with diameter $10$ (2 d.p.)?
A $10 \times 10$ square has a circle of diameter $10$ cut out. Remaining area (2 d.p.)?
A $10 \times 10$ square has a $4 \times 4$ square cut from one corner. Find the remaining area.