Logo and design problems

A question is this type if and only if it presents a real-world scenario for a logo or decorative design involving multiple geometric components (sectors, triangles, curves) requiring area or perimeter calculations.

7 questions · Standard +0.0

1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta
Sort by: Default | Easiest first | Hardest first
Edexcel P1 2021 October Q7
10 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-18_428_894_210_525} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows the design for a sign at a bird sanctuary.
The design consists of a kite \(O A B C\) joined to a sector \(O C X A\) of a circle centre \(O\).
In the design
  • \(O A = O C = 0.6 \mathrm {~m}\)
  • \(A B = C B = 1.4 \mathrm {~m}\)
  • Angle \(O A B =\) Angle \(O C B = 2\) radians
  • Angle \(A O C = \theta\) radians, as shown in Figure 3
Making your method clear,
  1. show that \(\theta = 1.64\) radians to 3 significant figures,
  2. find the perimeter of the sign, in metres to 2 significant figures,
  3. find the area of the sign, in \(\mathrm { m } ^ { 2 }\) to 2 significant figures.
Edexcel C12 2019 June Q8
10 marks Standard +0.3
8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de511cb3-35c7-4225-b459-a136b6304b78-20_547_463_269_735} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Diagram not drawn to scale Figure 2 shows the design for a company logo. The design consists of a triangle \(A B E\) joined to a sector \(B C D E\) of a circle with radius 6 cm and centre \(E\). The line \(A E\) is perpendicular to the line \(D E\) and the length of \(A E\) is 9 cm . The size of angle \(D E B\) is 3.5 radians, as shown in Figure 2.
  1. Find the length of the arc BCD. Find, to one decimal place,
  2. the perimeter of the logo,
  3. the area of the logo.
Edexcel C2 2009 January Q7
8 marks Standard +0.3
7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{12e54724-64a3-4dc0-b7d5-6ef6cc04124c-09_878_991_233_461} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The shape \(B C D\) shown in Figure 3 is a design for a logo. The straight lines \(D B\) and \(D C\) are equal in length. The curve \(B C\) is an arc of a circle with centre \(A\) and radius 6 cm . The size of \(\angle B A C\) is 2.2 radians and \(A D = 4 \mathrm {~cm}\). Find
  1. the area of the sector \(B A C\), in \(\mathrm { cm } ^ { 2 }\),
  2. the size of \(\angle D A C\), in radians to 3 significant figures,
  3. the complete area of the logo design, to the nearest \(\mathrm { cm } ^ { 2 }\).
Edexcel C2 2015 June Q4
8 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8a7593c3-4f0b-4351-afae-7bd98cfc351d-06_513_775_269_589} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sketch of a design for a scraper blade. The blade \(A O B C D A\) consists of an isosceles triangle \(C O D\) joined along its equal sides to sectors \(O B C\) and \(O D A\) of a circle with centre \(O\) and radius 8 cm . Angles \(A O D\) and \(B O C\) are equal. \(A O B\) is a straight line and is parallel to the line \(D C . D C\) has length 7 cm .
  1. Show that the angle \(C O D\) is 0.906 radians, correct to 3 significant figures.
  2. Find the perimeter of \(A O B C D A\), giving your answer to 3 significant figures.
  3. Find the area of \(A O B C D A\), giving your answer to 3 significant figures.
CAIE P1 2023 November Q4
6 marks Moderate -0.5
\includegraphics{figure_4} The diagram shows the shape of a coin. The three arcs \(AB\), \(BC\) and \(CA\) are parts of circles with centres \(C\), \(A\) and \(B\) respectively. \(ABC\) is an equilateral triangle with sides of length 2 cm.
  1. Find the perimeter of the coin. [2]
  2. Find the area of the face \(ABC\) of the coin, giving the answer in terms of \(\pi\) and \(\sqrt{3}\). [4]
Edexcel C2 Q3
5 marks Moderate -0.8
\includegraphics{figure_1} Figure 1 shows a logo \(ABD\). The logo is formed from triangle \(ABC\). The mid-point of \(AC\) is \(D\) and \(BC = AD = DC = 6\) cm. \(\angle BCA = 0.4\) radians. The curve \(BD\) is an arc of a circle with centre \(C\) and radius 6 cm.
  1. Write down the length of the arc \(BD\). [1]
  2. Find the length of \(AB\). [3]
  3. Write down the perimeter of the logo \(ABD\), giving your answer to 3 significant figures. [1]
OCR MEI C2 Q4
12 marks Standard +0.3
\emph{Arrowline Enterprises} is considering two possible logos: \includegraphics{figure_6}
  1. Fig. 10.1 shows the first logo ABCD. It is symmetrical about AC. Find the length of AB and hence find the area of this logo. [4]
  2. Fig. 10.2 shows a circle with centre O and radius 12.6 cm. ST and RT are tangents to the circle and angle SOR is 1.82 radians. The shaded region shows the second logo. Show that ST = 16.2 cm to 3 significant figures. Find the area and perimeter of this logo. [8]