KA-0083Perimeter and area of rectilinear shapes
3 points, difficulty 1 of 3Level 3–4about 45sA rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Find the other side before you find the area.
2The strategy
A rectangle has two sides of each length, so the perimeter is twice the sum of the two different sides. Use that to get the missing side, and only then multiply.
3The full solution
Twice the sum of the sides is 20, so the two sides add to 10. One is 6, so the other is 4, and the area is 6 x 4 = 24.
Solution— no shortcut on this one
The perimeter is 2 x (long + short) = 20, so the two different sides add to 10. One is 6, so the other is 4. The area is 6 x 4 = 24 square centimetres. The transferable idea: halve the perimeter first — it turns two sides into one addition instead of four.
Why this is on the test: Perimeter and area sit in the same question and pull in opposite directions, and forgetting that each side appears twice is the standard slip.