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Composite figures · triangle cut-out
P6 · Area & perimeter · PSLE Maths
Question
Mei Ling has a rectangular piece of coloured paper measuring 32 cm by 24 cm. She cuts away a right-angled triangular piece from one corner. The two perpendicular sides of the triangle along the edges of the rectangle are 18 cm and 14 cm. What is the area of the remaining paper?
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Hint
Find the area of the whole rectangle first, then the area of the right-angled triangle cut out, and subtract.
Show the answer and step-by-step explanation
Answer: Remaining area 642 cm²
- Understand the figure — This is a rectangle with a right-angled triangle cut out from the top right corner. To find the remaining area, use: area of rectangle − area of triangle cut out.
- Rectangle area — First, find the area of the whole piece of paper. Area of rectangle = length × breadth.
- Base and height — The part cut out is a right-angled triangle. Its two perpendicular sides are the base 18 cm and the height 14 cm.
- Triangle area — Area of a right-angled triangle = 1/2 × base × height. The area cut out is 1/2 × 18 × 14 = 126 cm².
- Subtract — Remaining area = area of the whole rectangle − area cut out. So, 768 − 126 = 642 cm².
- Write the answer — Therefore, the area of the remaining paper is 642 cm². 📌 Key idea: for a figure with a part cut out, find the area of the whole figure first, then subtract the area cut out.
Method: For a composite figure, use area of the whole figure − area of the part cut out. Area of a right-angled triangle = 1/2 × base × height.
Practice: 3 similar questions
- Siti has a rectangular sticker sheet measuring 30 cm by 20 cm. She cuts away a right-angled triangle from one corner. The two perpendicular sides of the triangle are 12 cm and 15 cm. What is the area of the remaining part?
Answer
510 cm² — Area of rectangle = 30 × 20 = 600 cm². Area of triangle cut out = 1/2 × 12 × 15 = 90 cm². Remaining area = 600 − 90 = 510 cm².
- Raju makes a rectangular card for the class noticeboard. It measures 45 cm by 28 cm. He cuts away a right-angled triangle from one corner. The two perpendicular sides of the triangle along the edges are 25 cm and 16 cm. What is the area of the remaining card?
Answer
1060 cm² — Area of rectangle = 45 × 28 = 1260 cm². Area of triangle cut out = 1/2 × 25 × 16 = 200 cm². Remaining area = 1260 − 200 = 1060 cm².
- Ali has a rectangular model board measuring 36 cm by 25 cm. He cuts away a right-angled triangle from the top right corner. The side of the triangle along the top edge is 16 cm. The other perpendicular side is along the right edge, from the top edge to a point 7 cm above the bottom edge. What is the area of the remaining board?
Answer
756 cm² — The perpendicular side on the right edge = 25 − 7 = 18 cm. Area of rectangle = 36 × 25 = 900 cm². Area of triangle cut out = 1/2 × 16 × 18 = 144 cm². Remaining area = 900 − 144 = 756 cm².
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