Mathematics 4024 · O Level · Area and perimeter

Area and perimeter — practice question

$ABCD$ forms a rectangle with $AB = 10$ cm and $AD = 12$ cm. $PQ$ runs parallel to $AB$ and $RS$ runs parallel to $AD$. The intersection of $PQ$ and $RS$ is $Y$. $BR = DP = x$ cm. A smaller rectangle and a square are shaded.
(a(i))[1]

In terms of $x$, write an expression for $AR$.

(a(ii))[1]

In terms of $x$, write an expression for $AP$.

(b)[3]

$\dfrac{\text{Area of shaded rectangle } ARYP}{\text{Area of rectangle } ABCD} = \frac{3}{4}$. Demonstrate that $x^2 - 22x + 30 = 0$.

(c)[3]

Find the solutions of $x^2 - 22x + 30 = 0$. Show your method and round your answers to 2 decimal places.

(d)[2]

Determine the total unshaded area inside rectangle $ABCD$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Answer: $10-x$.

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI