Geometry Basics
Answer all 15 questions to test your understanding. Your results will be shown at the end.
A triangular bracket has a horizontal base of 12 cm, a perpendicular height of 5 cm, and a sloping edge of 13 cm. An engineer needs its face area to estimate the coating required.
What area should the engineer use?
Two triangular fabric pieces have base–height measurements of 10 cm by 6 cm and 6 cm by 10 cm, respectively; both heights are perpendicular to their bases. The first piece also has a sloping edge measuring 8 cm.
Which statements about the pieces are justified? Select all that apply.
- Both pieces have an area of 30 cm².
- Using the first piece's 8 cm edge as its base allows its 6 cm height to remain unchanged.
- Rotating the first piece without resizing it leaves its area at 30 cm².
- Both pieces have an area of 60 cm².
A CAD drawing lists four triangular plates: P has base 14 cm and perpendicular height 3 cm; Q has base 8 cm and perpendicular height 9 cm; R has base 11 cm and perpendicular height 4 cm; S has base 7 cm and perpendicular height 10 cm.
Match each plate to its face area.
A rectangular equipment mat measures 2.4 m long and 75 cm wide. A purchasing form requires its area in square metres.
Which area belongs on the form?
A rectangular display changes from 12 cm by 5 cm to 24 cm by 2.5 cm. The designer is checking whether the amount of display material changes.
Assertion: The original and redesigned displays have the same area. Reason: The original and redesigned displays have the same perimeter.
A rectangular screen opening measures 8 cm by 5 cm. A frame extends 1 cm outward from every side, making the complete assembly 10 cm by 7 cm.
Which area calculations are correct? Select all that apply.
- The screen opening has an area of 40 cm².
- The complete assembly has an area of 70 cm².
- The frame alone has an area of 26 cm².
- The frame alone has an area of 30 cm².
A circular inspection cover measures 14 cm across its centre from edge to edge. A technician must record its face area exactly, without replacing π with a decimal.
What area should the technician record?
A parts catalogue lists four circular seals: A has radius 2 cm, B has diameter 6 cm, C has radius 5 cm, and D has diameter 8 cm. Their face areas must be recorded in terms of π.
Match each seal to its exact face area.
A circular sensor pad is redesigned from radius 3 cm to radius 6 cm. Both versions are flat discs, and the team is comparing their face areas.
Which statements correctly describe the redesign? Select all that apply.
- The redesigned pad has an area of 18π cm².
- The redesigned pad has an area of 36π cm².
- The original pad's area is one-quarter of the redesigned pad's area.
- The redesigned pad has an area of 12π cm².
A triangular support has two interior angles marked 48° and 67°. The drawing is not to scale, so the remaining angle cannot be reliably measured from the image.
What is the remaining interior angle?
One side of a triangular frame is extended, creating an exterior angle of 120° at vertex B. The interior angle at vertex A is 35°, and the interior angle at vertex C is unknown.
Assertion: The interior angle at C is 25°. Reason: The three interior angles of a triangle sum to 180°.
Four triangular brackets need angle checks: P has interior angles 90° and 34°; Q has interior angles 38° and 47°; R has a 45° exterior angle and a 20° interior angle at another vertex; S has a 44° apex angle and two equal base angles.
Match each bracket to the requested missing interior angle.
A triangular ventilation opening must have an area of 84 cm² and a base of 14 cm. The fabricator needs the perpendicular height, not the length of a sloping edge.
What perpendicular height meets the requirement?
A rectangular panel and a triangular panel must each have an area of 48 cm². The rectangle's width is 6 cm, and the triangle's base is 6 cm.
Which dimensions and comparisons are correct? Select all that apply.
- The rectangle's required length is 8 cm.
- The triangle's required perpendicular height is 8 cm.
- The triangle's required perpendicular height is 16 cm.
- The triangle's required height is twice the rectangle's required length.
Four panels need missing dimensions calculated: A is a rectangle of area 30 cm² and width 5 cm; B is a triangle of area 28 cm² and base 7 cm; C is a rectangle of area 45 cm² and width 5 cm; D is a triangle of area 15 cm² and base 6 cm.
Order the panels from smallest to largest missing dimension, using rectangle lengths and triangle perpendicular heights.