Mensuration:

The perimeter of a triangle is simply the total distance around it. You add up all three side lengths. For example, if a triangular plot of land in Ibadan has sides measuring 5m, 7m, and 8m, the perimeter would be 5 + 7 + 8 = 20m. This tells you how much fencing you'd need to enclose it.

Area measures the space inside the triangle. The basic formula is Area = ½ × base × height. The base is any side, and the height is the perpendicular distance from that side to the opposite corner. If a triangular piece of farmland has a base of 10m and height of 6m, its area is ½ × 10 × 6 = 30 square metres.

When you know all three sides but not the height, use Heron's formula: find the semi-perimeter (s) first, then Area = √[s(s-a)(s-b)(s-c)] where a, b, c are the sides.

Mensuration is about calculating areas and perimeters of shapes. For quadrilaterals like rectangles and trapezoids, you multiply length by width or use specific formulas based on their properties. Circles are different—you use π (pi) to find their area and circumference. The tricky part comes with composite figures, which combine multiple shapes together.

Imagine a plot of land shaped like a rectangle with a semicircular garden attached to one end. To find the total area, you'd calculate the rectangle's area separately, then add the semicircle's area. This is common in Nigerian real estate and architectural designs. Breaking complex shapes into simpler ones makes calculations manageable and less confusing.

When you look at a circle, an arc is simply the curved part of the circumference between two points. Think of it like the bend on a roundabout in Lagos—not the straight distance across, but the actual road you drive on. To find arc length, you use the formula: Arc length = (θ/360°) × 2πr, where θ is the angle at the centre and r is the radius.

A chord is different—it's the straight line connecting two points on the circle. The longest chord is always the diameter. For perimeters of sectors or segments, you add the arc length to the relevant straight edges. Imagine a slice of chin-chin; the perimeter includes the curved outer edge plus the two straight sides from the centre.

Practice sketching circles and labeling angles carefully.

A sector of a circle is the region bounded by two radii and an arc—imagine slicing a pie. The arc length is the curved edge, calculated using the formula: arc length = (θ/360°) × 2πr, where θ is the angle and r is the radius. The sector's area follows similarly: area = (θ/360°) × πr².

A segment is different—it's the region between a chord and the arc above it. Think of cutting a slice from a calabash of paint; the curved part you remove is a segment. Its area equals the sector area minus the triangle area formed by the two radii and chord.

For example, in Lagos, if a circular garden has radius 14 metres with a central angle of 90°, the sector area would be (90/360) × π × 14² square metres. These calculations appear frequently in JAMB questions about circular plots and decorative designs.

Think of mensuration as learning to measure three-dimensional shapes like boxes, spheres, and cylinders. Surface area is the total amount of space covering the outside of an object, while volume is how much space the object can hold inside.

Imagine a container of peak milk powder at home. The surface area includes all the metal around it, and the volume tells you how many litres of milk it holds. For a rectangular box with length, width, and height, you add up all six faces to get surface area, then multiply length × width × height for volume.

Different shapes need different formulas. A sphere uses 4πr² for surface area and (4/3)πr³ for volume. Cylinders use 2πrh + 2πr² for surface area and πr²h for volume. Practice substituting real numbers into these formulas repeatedly.

Mensuration is about calculating the surface area and volume of solid shapes. Think of it like finding how much paint you need for a box (surface area) or how much water it can hold (volume). The main shapes you'll encounter are cuboids (rectangular boxes), cylinders (like tin cans), cones (like ice cream cones), pyramids (like the ones in Egypt), and prisms (shapes that extend uniformly).

Each shape has specific formulas. A cuboid's volume is length × width × height. A cylinder's volume is πr²h. Cones and pyramids use one-third of their base area times height. Many Nigerian students struggle with remembering which formula applies to which shape, so practice identifying shapes first before calculating.

A sphere is simply a perfectly round 3D ball shape, like a football or orange. To find its surface area, you use the formula 4πr², and for volume, you use (4/3)πr³, where r is the radius. Composite figures combine two or more basic shapes together. For example, a water tank shaped like a cylinder with a hemispherical top is composite—you calculate the cylinder's volume and the hemisphere's volume separately, then add them.

Think about a typical Nigerian grain storage silo: it's usually cylindrical at the bottom with a conical roof on top. To find how much grain it holds, you'd calculate the cylinder's volume plus the cone's volume. The key strategy is breaking the complex shape into simpler parts you already know how to handle.

The distance between two points is simply how far apart they are on a coordinate plane. Think of it like measuring the straight-line distance between two locations on a map. When you have two points with coordinates like (x₁, y₁) and (x₂, y₂), you use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. This formula comes from the Pythagorean theorem. Imagine two buildings in Lagos: one at position (2, 3) and another at (5, 7). The distance between them would be √[(5-2)² + (7-3)²] = √[9 + 16] = √25 = 5 units.

The key idea is that you're creating a right-angled triangle between the two points and using the Pythagorean principle to find the hypotenuse—that's your distance.

Think of the Earth as a massive sphere, and mensuration helps us calculate distances and areas on its curved surface. Unlike flat geometry, the Earth's surface involves spherical calculations because our planet is roughly spherical in shape.

When measuring distances between cities like Lagos and Abuja, we use great circles—the shortest paths on a sphere's surface. This differs from measuring on a flat map. The Earth's radius is approximately 6,371 kilometers, and knowing this helps us find arc lengths between locations and surface areas of regions.

In JAMB questions, you'll often calculate distances between two points using latitude and longitude coordinates, or find how far apart two cities are along the Earth's surface. You might also determine the area of a spherical zone.