Geometry — Semester B
Free Practice · 10 Questions · 20 min
20:00 Exit
1
2
3
4
5
6
7
8
9
10
Question 1 of 10
TEKS 1A-1G Hard Calc Word
A composite figure is made of a rectangle (10 m × 6 m) with a semicircle attached to one of the shorter sides. What is the total area? (Use π ≈ 3.14)
A 64.7 m²
B 88.3 m²
C 74.1 m²
D 102.5 m²
Explanation
📌 Step 1: Break into simple shapes
Rectangle: 10 m × 6 m
Semicircle: radius = 6/2 = 3 m (attached to the 6 m side)

📌 Step 2: Calculate each area
Rectangle = 10 × 6 = 60 m²
Semicircle = ½πr² = ½ × 3.14 × 3² = ½ × 28.26 = 14.13 m²

📌 Step 3: Add them
Total = 60 + 14.13 = 74.13 ≈ 74.1 m²

💡 Strategy for composite figures: Always break them into shapes you know (rectangles, triangles, circles), calculate each, then add (or subtract for holes).
Question 2 of 10
TEKS 11A-11D Medium Calc Word Diagram
Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14) h = 15 cm r = 6 cm
A 339.1 cm³
B 565.2 cm³
C 1695.6 cm³
D 452.2 cm³
Explanation
📌 Step 1: Recall the cone volume formula
V = (1/3)πr²h

📌 Step 2: Plug in values
r = 6 cm, h = 15 cm
V = (1/3)(3.14)(36)(15)

📌 Step 3: Calculate step by step
3.14 × 36 = 113.04
113.04 × 15 = 1695.6
1695.6 / 3 = 565.2 cm³

💡 Common mistake: Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.
Question 3 of 10
TEKS 12A-12E Medium Calc Word Diagram
A tangent line touches circle O at point T. OT = 5 and the external point P is 13 units from the center O. What is the length of tangent segment PT? O T P 5 ? 13
A 14
B 8
C 12
D 10
Explanation
The tangent is perpendicular to the radius at the point of tangency. Using the Pythagorean theorem: PT = √(OP² − OT²) = √(13² − 5²) = √(169 − 25) = √144 = 12.
Question 4 of 10
TEKS 1A-1G Medium Calc Word Diagram
A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819) h = ? 55° 200 ft
A 141 feet
B 115 feet
C 186 feet
D 164 feet
Explanation
📌 Step 1: Identify the trig ratio
We know the hypotenuse (200 ft) and want the opposite side (height).
Use sine: sin = opposite / hypotenuse

📌 Step 2: Set up and solve
sin(55°) = h / 200
0.819 = h / 200
h = 200 × 0.819 = 163.8

📌 Answer: ≈ 164 feet

💡 Tip: Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.
Question 5 of 10
TEKS 1A-1G Easy Calc Word
A cylindrical water tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank? (Use π ≈ 3.14)
A 301.44 ft³
B 75.36 ft³
C 150.72 ft³
D 226.08 ft³
Explanation
📌 Step 1: Recall the volume formula for a cylinder
V = πr²h

📌 Step 2: Plug in the values
r = 3 ft, h = 8 ft, π ≈ 3.14
V = 3.14 × 3² × 8 = 3.14 × 9 × 8

📌 Step 3: Calculate
3.14 × 9 = 28.26
28.26 × 8 = 226.08 ft³

💡 Tip: Always check your units — volume is measured in cubic units (ft³, cm³, m³).
Question 6 of 10
TEKS 11A-11D Medium Calc Word Diagram
A swimming pool has the shape shown below — a rectangle with a semicircle on each end. Find the total area of the pool. (Use π ≈ 3.14) 20 m 10 m r = 5
A 356.0 m²
B 200.0 m²
C 278.5 m²
D 257.0 m²
Explanation
Rectangle area = 20 × 10 = 200 m².
Two semicircles = one full circle with r = 5: π × 5² = 3.14 × 25 = 78.5 m².
Total = 200 + 78.5 = 278.5 m².
Question 7 of 10
TEKS 3A-3D Hard Calc Word
Point Q(4, −1) is first reflected across the y-axis, then rotated 180° about the origin. What is the final image?
A (4, 1)
B (−4, 1)
C (−4, −1)
D (4, −1)
Explanation
📌 Step 1: Understand rigid motions (isometries)
Transformations that preserve BOTH size and shape:
✅ Translation (slide)
✅ Reflection (flip)
✅ Rotation (turn)

📌 Step 2: Non-rigid transformations
❌ Dilation — changes size
❌ Stretches/compressions — distort shape

📌 Answer: Translation preserves both size and shape.

💡 Key term: Rigid motions are also called "isometries" (iso = same, metry = measure).
Question 8 of 10
TEKS 1A-1G Medium Calc Word Diagram
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD? A B C D 16 22 AB ∥ DC AB ≠ DC
A Rhombus
B Trapezoid
C Parallelogram
D Rectangle
Explanation
A quadrilateral with exactly one pair of parallel sides is a trapezoid.
AB ∥ DC but AB ≠ DC (16 ≠ 22), confirming it is a trapezoid, not a parallelogram.
Question 9 of 10
TEKS 3A-3D Easy Calc Word Diagram
Which of the following figures has BOTH reflectional and rotational symmetry? A B C D
A B (Regular hexagon)
B C (Parallelogram)
C D (Arrow)
D A (Scalene triangle)
Explanation
📌 Step 1: Check each figure

A (Scalene triangle): No lines of symmetry, no rotational symmetry ✗
B (Regular hexagon): 6 lines of symmetry + rotational symmetry at 60° ✓
C (Parallelogram): No lines of symmetry, rotational symmetry at 180° only → partial ✗
D (Arrow): 1 line of symmetry (vertical) but no rotational symmetry ✗

📌 Answer: B (Regular hexagon)

💡 Tip: All regular polygons have BOTH reflectional AND rotational symmetry. The number of symmetry lines = number of sides.
Question 10 of 10
TEKS 1A-1G Easy Calc Word
A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?
A 392 in³
B 280 in³
C 448 in³
D 196 in³
Explanation
📌 Step 1: Identify the shape
A pizza box is a rectangular prism (cuboid).

📌 Step 2: Apply the volume formula
V = length × width × height
V = 14 × 14 × 2

📌 Step 3: Calculate
= 392 in³

💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!

Score
Correct
Wrong
Try Again Exit