Higher June 2024 Paper 3 Q18
18 \(ABCD\) is a quadrilateral.
The area of triangle \(ABC\) is 54 cm2
Calculate the area of triangle \(ACD\).
Give your answer correct to 3 significant figures. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 52.5 | P1 | for start of process to find length of \(AC\), eg \(\dfrac{1}{2} \times 17 \times AC \times \sin 35 = 54\) or \((AC =)\ 54 \div \left(\dfrac{1}{2} \times 17 \times \sin 35\right)\ (= 11.076\ldots)\) |
| P1 | for start of process to find \(AD\) or \(CD\), eg \(\dfrac{AD}{\sin 48} = \dfrac{\text{``}11.076\text{''}}{\sin 57}\) oe or \(\dfrac{AD}{\sin 48} = \dfrac{[AC]}{\sin 57}\) oe or \(\dfrac{CD}{\sin \text{``}75\text{''}} = \dfrac{\text{``}11.076\text{''}}{\sin 57}\) oe or \(\dfrac{CD}{\sin \text{``}75\text{''}} = \dfrac{[AC]}{\sin 57}\) oe | |
| P1 | for complete process to find \(AD\) or \(CD\) \((AD =)\ \dfrac{\text{``}11.076\text{''}}{\sin 57} \times \sin 48\ (= 9.81\ldots)\) or \((AD =)\ \dfrac{[AC]}{\sin 57} \times \sin 48\) or \((CD =)\ \dfrac{\text{``}11.076\text{''}}{\sin 57} \times \sin \text{``}75\text{''}\ (= 12.7\ldots)\) or \((CD =)\ \dfrac{[AC]}{\sin 57} \times \sin \text{``}75\text{''}\) | |
| P1 | for process to find area of triangle \(ACD\), eg \(\dfrac{1}{2} \times \text{``}11.076\text{''} \times \text{``}12.7\text{''} \times \sin 48\) or \(\dfrac{1}{2} \times [AC] \times [CD] \times \sin 48\) or \(\dfrac{1}{2} \times \text{``}11.076\text{''} \times \text{``}9.81\text{''} \times \sin \text{``}75\text{''}\) or \(\dfrac{1}{2} \times [AC] \times [AD] \times \sin \text{``}75\text{''}\) or \(\dfrac{1}{2} \times \text{``}9.81\text{''} \times \text{``}12.7\text{''} \times \sin 57\) or \(\dfrac{1}{2} \times [AD] \times [CD] \times \sin 57\) | |
| A1 | for answer in the range 52.4 to 52.52 |
Additional guidance
Check diagram for working throughout
Throughout \(\text{``}75\text{''} = 180 - 48 - 57\)
\([AC]\) must be a numerical value and clearly identified by labelling or on the diagram with no contradiction.
\([AC]\), \([AD]\), \([CD]\) must be numerical values and clearly identified by labelling or on the diagram with no contradiction.
If an answer is shown in the range in working and then incorrectly rounded award full marks