Plane geometry (polygons, triangles, angles) — ISEE Upper Mathematics Achievement practice questions

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Practice 138 Plane geometry (polygons, triangles, angles) questions in the app

What this topic is

Circles join polygons and triangles in Plane geometry (polygons, triangles, angles) within Mathematics Achievement.

Circumference equals two pi r and area equals pi r squared, so a question giving one usually wants the other, found by first solving for the radius. Composite figures are common: the area left after cutting shapes from a larger one equals the large area minus the pieces.

The Pythagorean theorem finds missing sides of right triangles, and familiar triples such as three, four, five save time. Shapes placed on a coordinate grid let side lengths be read from coordinates. Choices frequently include the diameter used in place of the radius.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A circle has circumference $18 π$ . What is the area of the circle?

81 π

✓ Correct

36 π

✗ Not this one

162 π

✗ Not this one

324 π

✗ Not this one

Show answer

Answer: A — $81 π$

Since $C = 2 π r$ , $18 π = 2 π r$ , so $r = 9$ . The area is $π r^{2} = π (9^{2}) = 81 π$ .

Question 2Mid

A square has side length 12 units. Four congruent right triangles are removed from the square, one from each corner. Each removed triangle has legs of length 3 units and 4 units along the sides of the square. What percent of the square’s original area remains?

83 \frac{1}{3} %

✓ Correct

80 %

✗ Not this one

87 \frac{1}{2} %

✗ Not this one

91 \frac{2}{3} %

✗ Not this one

Show answer

Answer: A — $83 \frac{1}{3} %$

The square’s area is $12 \cdot 12 = 144$ . Each removed triangle has area $\frac{1}{2} \cdot 3 \cdot 4 = 6$ , so the four triangles have total area 24. The remaining area is $144 - 24 = 120$ , and $\frac{120}{144} = \frac{5}{6} = 83 \frac{1}{3} %$ .

Question 3Mid

Three vertices of an axis-aligned rectangle are $(- 5, - 3)$ , $(1, - 3)$ , and $(1, 1)$ . What is the rectangle’s perimeter?

10✗ Not this one20✓ Correct22✗ Not this one24✗ Not this one

Show answer

Answer: B — 20

The horizontal and vertical side lengths are 6 and 4. Therefore the perimeter is $2 (6 + 4) = 20$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 138 Plane geometry (polygons, triangles, angles) questions in the app

Plane geometry (polygons, triangles, angles) — ISEE Upper Mathematics Achievement practice questions

What this topic is

Sample questions

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Mathematics Achievement