SHSAT EASY INTERMIDIATE AND
HARD QUESTIONS WITH ANSWERS
2022
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Killey
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(MOSTLY) SIMPLE (MOSTLY AREA) PROBLEMS
Tatiana Shubin
I. EASY PROBLEMS
1. (AJHSME 1995)
Figures I, II and III are squares. The perimeter of I
is 12 and the perimeter of II is 24. The perimeter of III is
A) 9 B) 18 C) 36 D) 72 E) 81
2. (AMC 8 2000)
Triangles ABC, ADE, and EFG are all
equilateral. Points D and G are midpoints of AC and AE, respectively. If AB = 4, what is
the perimeter of figure ABCDEFG?
A) 12 B) 13 C) 15 D) 18 E) 21
3. ( AJHSME, 1986)
The perimeter of the polygon shown is
A) 14 B) 20 C) 28 D) 48
E) cannot be determined from the information given
4. (AMC 8 2000)
In order for Mateen to walk a kilometer (1000 m) in his rectangular backyard, he must
walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen’s
backyard in square meters?
A) 40 B) 200 C) 400 D) 500 E) 1000
5. (AMC 8 1999)
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the
garden larger, while using the same fence, its shape is changed to a square. By how many
square feet does this enlarge the garden?
A) 100 B) 200 C) 300 D) 400 E) 500
6. (AJHSME 1998)
1
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Let PQRS be a square piece of paper. P is folded onto R and then Q is folded onto S. The
area of the resulting figure is 9 square inches. Find the perimeter of square PQRS.
A) 9 B) 16 C) 18 D) 24 E) 36
7. (AJHSME 1990)
The area of this figure is 100 cm2. (The figure consists of four
identical squares.) Its perimeter is
A) 20 cm B) 25 cm C) 30 cm D) 40 cm E) 50 cm
8. (AJHSME 1990)
What fraction of the square is shaded?
A) 1/3 B) 2/5 C) 5/12 D) 3/7 E) ½
9. (AJHSME 1994)
Each of the three large squares shown below is the same size. Segments that intersect the
sides of the squares intersect at the midpoints of the sides. How do the shaded areas of
these squares compare?
I II III
A) The shaded areas in all three are equal.
B) Only the shaded areas of I and II are equal.
C) Only the shaded areas of I and III are equal.
D) Only the shaded areas of II and III are equal.
E) The shaded areas of I, II and III are all different.
10. (AJHSME 1996)
(Figure is drawn NOT TO SCALE.)
Figure OPQR is a square. Point O is the origin, and point Q has coordinates (2, 2). What
are the coordinates for T so that the area of triangle RQT equals the area of square
OPQR?
2
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HARD QUESTIONS WITH ANSWERS
2022
written by
Killey
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school or uni and find the study material you need.
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(MOSTLY) SIMPLE (MOSTLY AREA) PROBLEMS
Tatiana Shubin
I. EASY PROBLEMS
1. (AJHSME 1995)
Figures I, II and III are squares. The perimeter of I
is 12 and the perimeter of II is 24. The perimeter of III is
A) 9 B) 18 C) 36 D) 72 E) 81
2. (AMC 8 2000)
Triangles ABC, ADE, and EFG are all
equilateral. Points D and G are midpoints of AC and AE, respectively. If AB = 4, what is
the perimeter of figure ABCDEFG?
A) 12 B) 13 C) 15 D) 18 E) 21
3. ( AJHSME, 1986)
The perimeter of the polygon shown is
A) 14 B) 20 C) 28 D) 48
E) cannot be determined from the information given
4. (AMC 8 2000)
In order for Mateen to walk a kilometer (1000 m) in his rectangular backyard, he must
walk the length 25 times or walk its perimeter 10 times. What is the area of Mateen’s
backyard in square meters?
A) 40 B) 200 C) 400 D) 500 E) 1000
5. (AMC 8 1999)
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the
garden larger, while using the same fence, its shape is changed to a square. By how many
square feet does this enlarge the garden?
A) 100 B) 200 C) 300 D) 400 E) 500
6. (AJHSME 1998)
1
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Let PQRS be a square piece of paper. P is folded onto R and then Q is folded onto S. The
area of the resulting figure is 9 square inches. Find the perimeter of square PQRS.
A) 9 B) 16 C) 18 D) 24 E) 36
7. (AJHSME 1990)
The area of this figure is 100 cm2. (The figure consists of four
identical squares.) Its perimeter is
A) 20 cm B) 25 cm C) 30 cm D) 40 cm E) 50 cm
8. (AJHSME 1990)
What fraction of the square is shaded?
A) 1/3 B) 2/5 C) 5/12 D) 3/7 E) ½
9. (AJHSME 1994)
Each of the three large squares shown below is the same size. Segments that intersect the
sides of the squares intersect at the midpoints of the sides. How do the shaded areas of
these squares compare?
I II III
A) The shaded areas in all three are equal.
B) Only the shaded areas of I and II are equal.
C) Only the shaded areas of I and III are equal.
D) Only the shaded areas of II and III are equal.
E) The shaded areas of I, II and III are all different.
10. (AJHSME 1996)
(Figure is drawn NOT TO SCALE.)
Figure OPQR is a square. Point O is the origin, and point Q has coordinates (2, 2). What
are the coordinates for T so that the area of triangle RQT equals the area of square
OPQR?
2
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