# Geometry Concepts

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### 1. If a rectangle has a perimeter of 24, what could be its length and width?

**A.** $L = 2,W = 12$

**B.** $L = 4,W = 20$

**C.** $L = 5,W = 7$

**D.** $L = 8,W = 3$


#### 2. P = 2(L + W) Formulate for perimeter of a rectangle with length, L, and width, W, is given above. If the perimeter of a rectangle has P = 28. What could length, L, and width, W, be?

**A.** $28 = 2(2 + 14)$

**B.** $28 = 2(7 + 21)$

**C.** $28 = 2(5 + 9)$

**D.** $28 = 2(4 + 7)$


#### 3. If the length of a rectangle is 4 more than its width and the perimeter is 52, find the width.

**A.** $w = 11$

**B.** $w = 12$

**C.** $w = 15$

**D.** $w = 24$


#### 4. If the rectangle has length x and width x − 2, what is the perimeter of the rectangle?

**A.** $2x - 2$

**B.** $2x - 4$

**C.** $4x - 2$

**D.** $4x - 4$


#### 5. A company plans to pave a rectangular parking lot behind an office building. If the length or the planned parking lot is 140 feet and the width is 84 feet, what is the area to be paved for this parking lot? (Area = length × width)

**A.** 11,760 ft.

**B.** 10,760 ft.

**C.** 9,760 ft.

**D.** 8,760 ft.


#### 6. The expressions x − 2 and x + 3 represent the length and width of a rectangle, respectively. If the area of rectangle is 24, what is the perimeter of the rectangle?

**A.** 20

**B.** 22

**C.** 24

**D.** 28


#### 7. A rectangular frame is 5 inches wide and 7 inches long. What is the outside perimeter of the frame?

**A.** 20 inches

**B.** 22 inches

**C.** 24 inches

**D.** 26 inches


#### 8. If two sides of a triangle are 2x − 5 and x + 3, and the perimeter is 4x − 1, what is the length of the third side?

**A.** $x + 3$

**B.** $2x - 1$

**C.** $x + 1$

**D.** $x - 1$


#### 9. If a triangle has side lengths x, x + 2, and x − 4, what is the perimeter of the triangle?

**A.** $3x + 3$

**B.** $2x - 1$

**C.** $2x + 1$

**D.** $3x - 2$


#### 10. What is the area of the triangle?

*Figure: a right triangle with legs $\sqrt{6}$ and $\sqrt{24}$.*

**A.** 6

**B.** 24

**C.** 36

**D.** 73


#### 11. In the triangle, if $c = 12$, what is the value of $a$?

![Triangle for question 11](assets/geometry/q11-triangle.png)

**A.** 3

**B.** 9

**C.** $3\sqrt{7}$

**D.** $9\sqrt{7}$


#### 12. An airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away. Let x be the angle the pilot takes to land the airplane at the beginning of the runway. Which equation is a correct way to calculate x?

**A.** $sin(x) = \frac{5,000}{7,000}$

**B.** $sin(x) = \frac{7,000}{5,000}$

**C.** $tan(x) = \frac{5,000}{7,000}$

**D.** $tan(x) = \frac{7,000}{5,000}$


#### 13. In the triangle, if $c = 7$, what is the value of $a$?

![Triangle for question 13](assets/geometry/q13-triangle.png)

**A.** $\sqrt{33}$

**B.** 3

**C.** $3\sqrt{7}$

**D.** 9


#### 14. What is the area of a square that has a perimeter of 24 feet?

**A.** 10

**B.** 16

**C.** 26

**D.** 36


#### 15. In the figure above, the larger square has sides of length a and the smaller square has sides of length b. What is the area of the shaded region in terms of a and b?

**A.** $a^2 - b^2$

**B.** $(a + b)^2$

**C.** $(a - b)^2$

**D.** ab


#### 16. The area of the square below is 36. What is the value of x?

**A.** 2

**B.** 4

**C.** 9

**D.** 12


#### 17. The area of a rectangle is 1,176 square inches and the width of the rectangle is 28 inches. What is the length of the rectangle? (Area = length x width)

**A.** 21 inches

**B.** 42 inches

**C.** 560 inches

**D.** 1,148 inches


#### 18. A small cube has a side length of 2. How many small cubes are needed to fill a box with the following dimensions: length = 16, width = 12, height = 10?

**A.** 240

**B.** 120

**C.** 160

**D.** 25


#### 19. The surface area of a right rectangular prism can be found by finding the sum of the area of each of the faces of the prism. What is the surface area of a right rectangular prism with length 4 centimeters (cm), width 9 cm, and height 3 cm? (Area of a rectangle is equal to length times width.)

**A.** $75 cm^2$

**B.** $108 cm^2$

**C.** $120 cm^2$

**D.** $150 cm^2$


#### 20. Which is the volume of the rectangular solid shown above (V = L × W × H)

**A.** $160 in^3$

**B.** $128 in^3$

**C.** $64 in^3$

**D.** $32 in^3$


#### 21. In the figure, what is the average (arithmetic mean) of x, y, w, and z?

**A.** 90

**B.** 100

**C.** 120

**D.** It can’t be determined


#### 22. The dimensions of a room are shown, what is the area?

*Figure required: an irregular room outline labeled 14 ft, 14 ft, 18 ft, 8 ft, and 6 ft.*

**A.** $112 ft^2$

**B.** $196ft^2$

**C.** $220 ft^2$

**D.** $252 ft^2$


#### 23. The dimensions of a room are shown, what is the area?

*Figure required: an L-shaped room with dimensions labeled in terms of x.*

**A.** $14x + 2$

**B.** $12x + 2$

**C.** $10x^2$

**D.** $10x^2 + 2x$


#### 24. In an isosceles triangle, the base angles measure 65°. Which of the following expression is a way to calculate the measure the third angle?

**A.** $180^\circ + 65^\circ$

**B.** $180^\circ - 65^\circ$

**C.** $180^\circ + 2(65^\circ)$

**D.** $180^\circ - 2(65^\circ)$


#### 25. Figure 2 is a 90° clockwise rotation of Figure 1. Which angle in Figure 2 corresponds to ∠A in Figure 1?

**A.** $∠W$

**B.** ∠X

**C.** ∠Y

**D.** ∠Z


#### 26. The small base of an isosceles trapezoid is x cm long. The large base is 3 cm shorter than twice the small base. Each remaining side is 2 cm longer than the small base. If the perimeter is 26 cm, which of the following is true?

**A.** $4x - 3 = 26$

**B.** $4x -1 = 26$

**C.** $5x - 1 = 26$

**D.** $5x + 1 = 26$


#### 27. If the length of a rectangle, L, is 3 less than twice the width, W, which of the following gives the length of the rectangle in terms or width.

**A.** $L = 3 - 2W$

**B.** $L = 2W - 3$

**C.** $L = 3W - 2$

**D.** $L = 2 - 3W$