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Plane geometry (area, perimeter, circles) — SSAT Upper practice questions

Plane geometry (area, perimeter, circles) on the SSAT Upper Quantitative (Math) section covers rectangle area and perimeter, circle area including the region between two circles that share a center, and angle facts such as a straight angle. A student has to turn an area of 84 square units and a width of 7 units into a perimeter, find a missing radius when the area between the circles is 45π square units and the radii differ by 3 units, and complete a straight angle when one part is 75 degrees. Items are multiple choice; choices are usually numbers or π expressions, with traps that mix area and perimeter or drop π.

  • Section: Quantitative (Math) 50 questions on the paper
  • 138 practice questions in the app

Sample questions

Question 1

A straight angle is divided into two smaller angles. One angle measures 75∘75^\circ. What is the measure of the other angle?

  1. A95∘95^\circ
  2. B105∘105^\circ
  3. C110∘110^\circ
  4. D115∘115^\circ
  5. E120∘120^\circ
Show answer

Answer: B — 105∘105^\circ

The two smaller angles add to 180∘180^\circ, so the other angle is 180∘−75∘=105∘180^\circ-75^\circ=105^\circ.

Question 2

Two circles have the same center. The radius of the larger circle is 3 units more than the radius of the smaller circle. The area between the two circles is 45π45\pi square units. What is the radius of the smaller circle?

  1. A4
  2. B5
  3. C6
  4. D7
  5. E9
Show answer

Answer: C — 6

Let the smaller radius be rr and the larger radius be RR. Since R−r=3R-r=3 and π(R2−r2)=45π\pi(R^2-r^2)=45\pi, we have (R−r)(R+r)=45(R-r)(R+r)=45. Thus 3(R+r)=453(R+r)=45, so R+r=15R+r=15. Solving R−r=3R-r=3 and R+r=15R+r=15 gives r=6r=6.

Question 3

A rectangle has an area of 84 square units and a width of 7 units. What is the perimeter of the rectangle?

  1. A24
  2. B31
  3. C36
  4. D38
  5. E42
Show answer

Answer: D — 38

The missing length is 84÷7=1284\div7=12 units because area equals length times width. The perimeter is then 2(12+7)=382(12+7)=38 units.

Practice 138 Plane geometry (area, perimeter, circles) questions in the app

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