Math explorers

Plane Figures and Coordinate Geometry

Grade 6Geometry

Learn with worked examples, then try the questions below.

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1Area of a triangle

A triangle is half a parallelogram with the same base and perpendicular height. Height is measured at a right angle to the base.

Worked exampleA = ½ × b × h = ½ × 10 × 6 = 30 cm²

Do not use a sloping side as the height unless it is perpendicular to the base.

For a parallelogram, multiply base by perpendicular height. Split a composite shape into simple shapes, then add or subtract their areas.

Worked exampleParallelogram: 8 × 5 = 40 cm²

A 10 × 8 rectangle with a 4 × 3 corner removed has area 80 − 12 = 68 cm².

Plot each ordered pair (x, y), connect the vertices in order, and close the shape. Right and up are positive; left and down are negative.

Worked exampleRectangle: (−3, 2), (4, 2), (4, −2), (−3, −2)

The four vertices lie in quadrants II, I, IV, and III respectively. Its horizontal sides have matching y-coordinates.

Find horizontal and vertical distances by subtracting coordinates. Distances are positive, even when coordinates are negative.

Worked exampleWidth: 4 − (−3) = 7; height: 2 − (−2) = 4

The rectangle has area 7 × 4 = 28 square units. Reflecting a point across the x-axis changes only the sign of y.

Question 1 of 5

A triangle has base 12 cm and perpendicular height 5 cm. What is its area?

Need a hint?

Use half the product of base and height.