Lessons · Teaching · area, volume, angles and the right-angled triangle
Area, volume, angles and the right-angled triangle
The geometry asked is perimeter and area of rectangles, triangles and circles; volume of boxes and cylinders; angle facts on a straight line, around a point and in a triangle; and Pythagoras. Formulas may or may not be given, so knowing the common ones is worth the ten minutes it takes.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Geometry on this test is mostly one formula plus one careful reading of the question. The marks are lost on units and on reading, not on the geometry: a question giving a radius and asking about diameter, or giving centimetres and asking for square metres, catches more candidates than any theorem does.
How to think about it
Write the formula down before putting numbers in it. Label what you were given and what was asked, in words, including the unit. Then check the unit of the answer: a length is in units, an area in square units, a volume in cubic units, and an answer with the wrong kind of unit is wrong whatever the number is.
Worked example
Rectangle 8 by 5: perimeter 2 x (8 + 5) = 26, area 8 x 5 = 40One is a length and one is an area. Different units, different formulas, easy to swap under pressure.
Circle of radius 3: area is pi x 3 x 3 which is about 28.3, circumference is 2 x pi x 3 which is about 18.8Radius, not diameter. Half the questions here give you the diameter on purpose.
Angles in a triangle add to 180, so 50 and 60 leave 7050 + 60 = 110 and 180 - 110 = 70.
Right-angled triangle with legs 3 and 4: hypotenuse is the square root of 9 + 16, which is 5The 3, 4, 5 triangle appears constantly, and so do 5, 12, 13 and 6, 8, 10.
Your turn
Name the unit kind an area answer must carry.
An area is measured in units
Solve one, graded on the server
The trap
Using the diameter where the formula wants the radius. Every circle formula on this test takes the radius, and questions supply the diameter far more often than chance would suggest.