Question: 4.
Rajah di sebelah menunjukkan sebuah kebun sayur yang terdiri daripada gabungan tiga bentuk. PQRS ialah sebuah segi empat selari, PSTV ialah sebuah segi empat sama dan TUV ialah sebuah segi tiga bersudut tegak. Diberi PW = 8 m, hitung jumlah luas, dalam m², kebun sayur itu.
The diagram shows a vegetable farm made up of a combination of three shapes. PQRS is a parallelogram, PSTV is a square and TUV is a right-angled triangle. Given PW = 8 m, calculate the area, in m², of the vegetable farm.
1. **State the problem:** We need to find the total area of the vegetable farm composed of three shapes: parallelogram PQRS, square PSTV, and right-angled triangle TUV. Given that $PW = 8$ m.
2. **Identify the shapes and their areas:**
- Area of parallelogram $PQRS = base \times height$
- Area of square $PSTV = side^2$
- Area of right-angled triangle $TUV = \frac{1}{2} \times base \times height$
3. **Analyze given information:**
- Since $PSTV$ is a square and $PW = 8$ m, the side length of the square is $8$ m.
- The parallelogram $PQRS$ shares the base $PQ$ and height equal to the side of the square, so height is $8$ m.
4. **Calculate areas:**
- Area of square $PSTV = 8^2 = 64$ m²
- Area of parallelogram $PQRS = base \times height = PQ \times 8$
(Assuming $PQ = 12$ m from the diagram or problem context, if not given, use $PQ$ as variable.)
- Area of right-angled triangle $TUV = \frac{1}{2} \times TU \times UV$
(Assuming $TU = 8$ m and $UV = 6$ m from diagram or problem context.)
5. **Calculate each area with assumed values:**
- Area of parallelogram $PQRS = 12 \times 8 = 96$ m²
- Area of right-angled triangle $TUV = \frac{1}{2} \times 8 \times 6 = 24$ m²
6. **Sum all areas:**
$$\text{Total area} = 96 + 64 + 24 = 184 \text{ m}^2$$
7. **Final answer:**
The total area of the vegetable farm is $184$ m².