Calculate area and perimeter for triangles, quadrilaterals, and composite figures built from them — the formulas are simple, but composite figures require breaking the shape apart correctly first. Every question comes with a written walkthrough of exactly how the figure was split.
A triangle or parallelogram's height is the perpendicular distance to the base, not the length of a slanted side — using the wrong one gives a plausible-looking but wrong area.
Adding side lengths when the question asks for area, or multiplying dimensions when it asks for perimeter, produces a numerically real answer that answers the wrong question.
When two shapes share an edge inside a composite figure, that shared edge counts toward area calculations for both pieces but shouldn't be counted twice in the outer perimeter.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
Find the area of a triangle with base 12 cm and height 7 cm.
A — 42 cm². Area of a triangle is ½ × base × height: ½ × 12 × 7 = 42 cm². 84 cm² (B) comes from forgetting the ½ factor — computing base × height directly, which is the formula for a parallelogram, not a triangle.
A trapezoid has parallel sides of length 8 cm and 14 cm, and a height of 5 cm. Find its area.
A — 55 cm². The trapezoid area formula is ½(b₁+b₂)h: ½(8+14)(5) = ½(22)(5) = 55 cm². 110 cm² (B) comes from forgetting the ½ factor entirely — computing (8+14)×5 directly, as if for a rectangle. 27.5 cm² (D) comes from applying the ½ factor twice, halving the correct answer again by mistake.
A rectangular garden measuring 10 m by 14 m has a semicircular flower bed of radius 5 m built along one of the 10 m sides, extending outward. Find the total area enclosed by the garden and the flower bed. (Use π ≈ 3.14)
A — 179.25 m². Split the composite figure into its two pieces: the rectangle's area is 10 × 14 = 140 m², and the semicircle's area is ½πr² = ½ × 3.14 × 25 = 39.25 m². Adding them gives 140 + 39.25 = 179.25 m². 218.5 m² (B) comes from using the full circle's area (πr² = 78.5) instead of halving it for the semicircle: 140 + 78.5 = 218.5.
Area and perimeter problems are formula-recall wearing a geometry disguise — the fastest gains come from correctly identifying which shape, or combination of shapes, you're actually looking at.
Draw the figure and label every given measurement, splitting composite shapes into pieces on paper before writing a single formula. Untimed practice is where that habit gets built.
Move to timed sessions once shape identification and formula recall are instant. Composite figures run longer since there's more than one piece to compute.
Pair area and perimeter with circles in a mock — composite figures often combine straight-edged shapes with circular ones.
Already have an account? Sign in →