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)
A88.3 m²
B64.7 m²
C74.1 m²
D102.5 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
Florida standards 7A-7BMedium Calc Word Diagram
A tree casts a shadow 18 feet long. At the same time, a 5-foot-tall fence post casts a shadow 3 feet long. How tall is the tree?
A24 feet
B36 feet
C27 feet
D30 feet
Explanation
The tree and fence post form similar triangles with their shadows (same sun angle). tree height / tree shadow = fence height / fence shadow h / 18 = 5 / 3 h = 18 × 5/3 = 30 feet.
Question 3 of 10
Florida standards 8A-8BHard Calc Word Diagram
In right triangle ABC, an altitude CD is drawn from the right angle C to hypotenuse AB. If AD = 5 and DB = 12, what is the length of CD?
A2√15 ≈ 7.75
B√17 ≈ 4.12
C8.5
D√85 ≈ 9.22
Explanation
The altitude to the hypotenuse is the geometric mean of the two segments: CD = √(AD × DB) = √(5 × 12) = √60 = 2√15 ≈ 7.75.
Question 4 of 10
Florida standards 3A-3DEasy Calc Word Diagram
Which of the following figures has BOTH reflectional and rotational symmetry?
AB (Regular hexagon)
BA (Scalene triangle)
CD (Arrow)
DC (Parallelogram)
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 5 of 10
Florida standards 4A-4DEasy Calc Word Diagram
Jake claims: "If a quadrilateral has four right angles, then it must be a square." Which figure below is a counterexample?
ARectangle
BSquare
CTrapezoid
DRhombus
Explanation
A rectangle has four right angles but is NOT necessarily a square (it can have unequal side lengths). The rectangle with sides 90×60 is a counterexample to Jake's claim.
Question 6 of 10
Florida standards 1A-1GMedium Calc Word Diagram
A zip-line connects the top of a 40-foot platform to a point on the ground 75 feet away. What is the length of the zip-line cable?
A95 feet
B75 feet
C85 feet
D80 feet
Explanation
📌 Step 1: Identify the right triangle The platform height (40 ft), ground distance (75 ft), and cable form a right triangle.
💡 Tip: This is a multiple of the 8-15-17 Pythagorean triple (×5 = 40-75-85).
Question 7 of 10
Florida standards 12A-12EMedium 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?
A10
B12
C8
D14
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 8 of 10
Florida standards 11A-11DMedium Calc Word Diagram
Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14)
A565.2 cm³
B1695.6 cm³
C339.1 cm³
D452.2 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)
💡 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 9 of 10
Florida standards 6A-6EEasy Calc Word Diagram
In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C?
A70°
B75°
C60°
D50°
Explanation
📌 Step 1: Recall the Triangle Angle Sum Theorem All angles in a triangle add up to 180°.
📌 Step 2: Set up the equation ∠A + ∠B + ∠C = 180° 55° + 65° + ∠C = 180°
📌 Step 3: Solve ∠C = 180° − 55° − 65° = 60°
💡 Quick check: 55 + 65 + 60 = 180° ✓
Question 10 of 10
Florida standards 1A-1GMedium 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)
A186 feet
B164 feet
C115 feet
D141 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.