Perimeter
Rectangle 12 × 5 cm.
Perimeter = 2 × (length + width) = 2 × (12 + 5) = 2 × 17 = 34 cm
100: Triangle base 10 cm, height 4 cm. Find area.
Area = ½ × base × height = 0.5 × 10 × 4 = 20 cm².
Rectangle area 60 cm², width 5 cm. Find length.
Length = area ÷ width = 60 ÷ 5 = 12 cm.
Plot points A(1,1), B(4,1), C(4,3). Shape?
Points show two perpendicular sides (AB horizontal, BC vertical) and AC slanted → a right-angled triangle (right angle at B).
Check if triangle with sides 8,11,13 is valid.
Check sums: 8 + 11 = 19 > 13 ✓, 8 + 13 = 21 > 11 ✓, 11 + 13 = 24 > 8 ✓.
All true → valid triangle
Rectangle 17 × 8 cm.
Walk around outer edges: 12 + 8 + 5 + 12 + 8 + 5 = 50 cm.
(Or think: total top = 12+8, bottom = 12+8, plus two outer verticals 5 + 5 → 2×20 + 10 = 50.)
Answer: 50 cm.
200: Rectangle 10×7 cm. Find area.
Area = 10 × 7 = 70 cm².
Rectangle area 120 cm², width 10 cm. Find length.
Length = 120 ÷ 10 = 12 cm.
Points A(1,2), B(6,2), C(6,5), D(1,5). Identify shape.
Opposite sides equal and parallel, adjacent sides perpendicular → rectangle.
Rectangle 12×6 + semicircle diameter 12 cm. Total area?
Same as Missing Dimensions Q400: 128.52 cm².
Composite shape: 12×5 and 8×5 rectangles joined along 5 cm side. Perimeter?
Walk around outer edges: 12 + 8 + 5 + 12 + 8 + 5 = 50 cm.
(Or think: total top = 12+8, bottom = 12+8, plus two outer verticals 5 + 5 → 2×20 + 10 = 50.)
Answer: 50 cm.
Triangle base 14 cm, area 84 cm². Find height.
84 = ½ × 14 × h ⇒ 84 = 7h ⇒ h = 12 cm.
Parallelogram base 16 cm, area 128 cm². Find height.
Height = area ÷ base = 128 ÷ 16 = 8 cm.
Find area of the shape above.
Width = 6 − 1 = 5. Height = 5 − 2 = 3. Area = 5 × 3 = 15 square units.
Composite: rectangle 14×9 + triangle base 14, height 11. Total area?
Rectangle = 14 × 9 = 126 cm². Triangle = ½ × 14 × 11 = 7 × 11 = 77 cm². Total = 126 + 77 = 203 cm².
Rectangle has perimeter 48 cm and width 10 cm. Find length.
48 = 2 × (L + 10) ⇒ L + 10 = 24 ⇒ L = 14 cm.
Composite: Rectangle 10×7 + square 7×7 on top. Total area?
Rectangle = 10 × 7 = 70 cm². Square = 7 × 7 = 49 cm². Total = 70 + 49 = 119 cm².
Rectangle 12×6 + semicircle diameter 12 cm. Total area?
Rectangle area = 12 × 6 = 72 cm².
Full circle radius = 6 → circle area = πr² = 3.14 × 36 = 113.04 cm².
Semicircle area = 113.04 ÷ 2 = 56.52 cm².
Total = 72 + 56.52 = 128.52 cm².
Triangle P(3,1), Q(7,1), R(7,6) → translate 3 right, 2 up. New coordinates?
Add (3,2) to each:
P′ = (3+3, 1+2) = (6,3)
Q′ = (7+3, 1+2) = (10,3)
R′ = (7+3, 6+2) = (10,8)
Circle area 254.34 cm². Find radius and circumference.
Radius from earlier = 9 cm.
Circumference = 2πr = 2 × 3.14 × 9 = 6.28 × 9 = 56.52 cm.
Rectangle 8×6 cm has same area as a square. Find square side.
Rectangle area = 8 × 6 = 48 cm². Square side = √48 = √(16×3) = 4√3 ≈ 6.93 cm (exact: 434\sqrt343 cm).
Circle area 254.34 cm². Find radius.
Clue: Pi = 3.14159265358971567
Area =πr2= \pi r^2=πr2. So r=Aπ=254.343.14r = \sqrt{\dfrac{A}{\pi}} = \sqrt{\dfrac{254.34}{3.14}}r=πA=3.14254.34.
Compute 254.34 ÷ 3.14 = 81 → r=81=9 cmr = \sqrt{81} = \mathbf{9\text{ cm}}r=81=9 cm.
Rectangle + semicircle composite area 190.5 cm², rectangle width 8 cm. Find rectangle length.
Let rectangle area = 8L. Semicircle area = ½ π (L/2)² = πL28 \dfrac{\pi L^2}{8}8πL2.
So 8L+πL28=190.58L + \dfrac{\pi L^2}{8} = 190.58L+8πL2=190.5. Using π = 3.14:
Multiply by 8 → 64L+3.14L2=152464L + 3.14L^2 = 152464L+3.14L2=1524. Rearranged: 3.14L2+64L−1524=03.14L^2 + 64L - 1524 = 03.14L2+64L−1524=0.
Solve quadratic: discriminant =642−4(3.14)(−1524)=4096+19141.44=23237.44=64^2 - 4(3.14)(-1524)=4096 + 19141.44 = 23237.44=642−4(3.14)(−1524)=4096+19141.44=23237.44.
23237.44≈152.44\sqrt{23237.44}\approx 152.4423237.44≈152.44.
Positive root: L=−64+152.442×3.14≈88.446.28≈14.08 cmL = \dfrac{-64 + 152.44}{2\times3.14} \approx \dfrac{88.44}{6.28} \approx \mathbf{14.08\ \text{cm}}L=2×3.14−64+152.44≈6.2888.44≈14.08 cm (rounded to 2 d.p.).
In simple terms, answer is 190.5cm2 :)
Quadrilateral A(–2,1), B(6,1), C(7,8), D(–1,8). Prove trapezium, find area.
Check slopes / parallelism: AB from y=1 (−2→6) is horizontal (y=1). DC from y=8 (−1→7) is horizontal (y=8). So AB ∥ DC (both horizontal). AD slope = (8−1)/(−1+2) = 7/1 = 7; BC slope = (8−1)/(7−6) = 7/1 = 7 ⇒ AD ∥ BC as well.
So both pairs of opposite sides are parallel ⇒ it is a parallelogram (and hence also meets the loose definition of trapezium).
Base length AB = 6 − (−2) = 8. Height = vertical distance between y = 1 and y = 8 = 7.
Area = base × height = 8 × 7 = 56 square units.
Triangle sides 8,11,13. Determine type (right, isosceles, scalene).
Check for right angle: 8² + 11² = 64 + 121 = 185; 13² = 169 → not equal ⇒ not right-angled.
All three sides different ⇒ scalene. (So final: scalene, non-right triangle.)