MSE2183 Assignment 3 2026
DUE 23 JULY 2026
Question 2: Lesson 4 – Volume and Area
2.1
The second rectangle has sides 2a and b/2.
Area of first rectangle: A1
=a×b
b
Area of second rectangle: A2 = 2a ×
2
= ab
The areas are always equal for all a > 0, b > 0. (The rectangles are equal in area.)
2.2
Regular dodecagon (12 sides), each side = 7 cm.
Perimeter = 12 × 7 = 84 cm.
2.3 Self-assessment 4.1 (b) and (d)
b) Parallelogram (rhombus-like, but general parallelogram): sides a = 5.8 cm, height h = 5.26 cm.
Perimeter = 2(a + a) = 4a = 4 × 5.8 = 23.2 cm (opposite sides equal).
Area = base × height = 5.8 × 5.26 = 30.508 cm².
d) Regular pentagon: side s = 6.1 cm, apothem a = 4.198 cm.
Perimeter = 5s = 5 × 6.1 = 30.5 cm.
1 1
Area = 2 × perimeter × apothem = 2
× 30.5 × 4.198 ≈ 64.00 cm² (exact calc: 64.0099 ≈ 64.01
cm²).
DUE 23 JULY 2026
Question 2: Lesson 4 – Volume and Area
2.1
The second rectangle has sides 2a and b/2.
Area of first rectangle: A1
=a×b
b
Area of second rectangle: A2 = 2a ×
2
= ab
The areas are always equal for all a > 0, b > 0. (The rectangles are equal in area.)
2.2
Regular dodecagon (12 sides), each side = 7 cm.
Perimeter = 12 × 7 = 84 cm.
2.3 Self-assessment 4.1 (b) and (d)
b) Parallelogram (rhombus-like, but general parallelogram): sides a = 5.8 cm, height h = 5.26 cm.
Perimeter = 2(a + a) = 4a = 4 × 5.8 = 23.2 cm (opposite sides equal).
Area = base × height = 5.8 × 5.26 = 30.508 cm².
d) Regular pentagon: side s = 6.1 cm, apothem a = 4.198 cm.
Perimeter = 5s = 5 × 6.1 = 30.5 cm.
1 1
Area = 2 × perimeter × apothem = 2
× 30.5 × 4.198 ≈ 64.00 cm² (exact calc: 64.0099 ≈ 64.01
cm²).
