Solution:
\(C = \pi \times d\)
\(C = 3.14 \times 10 = 31.4\)
Answer: 31.4 cm
6
Calculate the Area of a triangle with a base of 12 mm and a height of 7 mm.
Solution:
\(A = \frac{1}{2} \times b \times h\)
\(A = 0.5 \times 12 \times 7\)
\(A = 6 \times 7 = 42\)
Answer: 42 mm²
GEOMETRY WORKSHEET - ANSWER KEY Page 2 of 7
PART 1 SOLUTIONS (CONTINUED)
7
A parallelogram has a base of 15 cm and an altitude (height) of 4 cm. What is its Area?
Solution:
\(A = b \times h\)
\(A = 15 \times 4 = 60\)
Answer: 60 cm²
8
Calculate the Area of a trapezoid with bases of 5 in and 9 in, and a vertical height of 6 in.
Solution:
\(A = \frac{1}{2} \times (b_1 + b_2) \times h\)
\(A = 0.5 \times (5 + 9) \times 6\)
\(A = 0.5 \times 14 \times 6 = 42\)
Answer: 42 in²
9
What is the Circumference of a circle with a radius of 3 m? (Use π = 3.14)
Solution:
\(C = 2 \times \pi \times r\)
\(C = 2 \times 3.14 \times 3\)
\(C = 6 \times 3.14 = 18.84\)
Answer: 18.84 m
10
Calculate the total Area of a circle with a radius of 10 in. (Use π = 3.14)
Solution:
\(A = \pi \times r^2\)
\(A = 3.14 \times 10^2\)
\(A = 3.14 \times 100 = 314\)
Answer: 314 in²
GEOMETRY WORKSHEET - ANSWER KEY Page 3 of 7
PART 2 WORD PROBLEMS SOLUTIONS
11
A triangular flag has a base of 15 ft and a height of 8 ft. What is the area of the flag?
Solution:
\(A = \frac{1}{2} \times b \times h\)
\(A = 0.5 \times 15 \times 8\)
\(A = 0.5 \times 120 = 60\)
Answer: 60 ft²
12
A flat plate has a base of 7.5 cm and a height of 4 cm. What is its area?
Solution:
\(A = b \times h\)
\(A = 7.5 \times 4 = 30\)
Answer: 30 cm²
13
Circular pool, diameter = 12 m. Safety fence length = ? (Use π = 3.14)
Solution:
\(C = \pi \times d\)
\(C = 3.14 \times 12 = 37.68\)
Answer: 37.68 m
14
Canvas sail, base = 6 m, height = 15 m. Total canvas area = ?
Solution:
\(A = \frac{1}{2} \times b \times h\)
\(A = 0.5 \times 6 \times 15 = 45\)
Answer: 45 m²
GEOMETRY WORKSHEET - ANSWER KEY Page 4 of 7
PART 2 WORD PROBLEMS & MISSING DIMENSIONS SOLUTIONS
15
Trapezoid desk, bases = 3 ft and 5 ft, height = 2.5 ft. Area = ?
Solution:
\(A = \frac{1}{2} \times (b_1 + b_2) \times h \implies A = 0.5 \times (3 + 5) \times 2.5 \implies A = 4 \times 2.5 = 10\)
Final Answer: 10 ft²
16
Parallelogram patio, base = 20 yd, height = 12 yd. Area = ?
Solution:
\(A = b \times h \implies A = 20 \times 12 = 240\)
Final Answer: 240 yd²
17
Area = 24 cm². Base = 8 cm. Solve for vertical height.
Solution:
\(A = \frac{1}{2} b h \implies 24 = \frac{1}{2} \times 8 \times h \implies 24 = 4h \implies h = 24 \div 4 = 6\)
Final Answer: 6 cm
GEOMETRY WORKSHEET - ANSWER KEY Page 5 of 7
PART 3 BACKWARD CALCULATIONS SOLUTIONS
18
Area = 80 in². Height = 10 in. Calculate length of base.
Solution:
\(A = b \times h \implies 80 = b \times 10 \implies b = 80 \div 10 = 8\)
Final Answer: 8 in
19
Circumference = 31.4 ft. Find the radius. (Use π = 3.14)
Solution:
\(C = 2 \pi r \implies 31.4 = 2 \times 3.14 \times r \implies 31.4 = 6.28r \implies r = 5\)
Final Answer: 5 ft
20
Area = 35 m². Bases = 6 m and 8 m. Solve for height.
Solution:
\(A = \frac{1}{2} (b_1 + b_2)h \implies 35 = 0.5 \times (6 + 8) \times h \implies 35 = 7h \implies h = 5\)
Final Answer: 5 m
GEOMETRY WORKSHEET - ANSWER KEY Page 6 of 7
PART 4: SURFACE AREA OF PRISMS SOLUTIONS
Rectangular Prism: \(SA = 2(lw + lh + wh)\) • Triangular Prism: Add the areas of the 2 triangular bases and 3 rectangular faces.
21
Find Surface Area of Rectangular Prism: \(l=5\text{ cm}\), \(w=3\text{ cm}\), \(h=4\text{ cm}\).
Step-by-Step Solution:
\(SA = 2(lw + lh + wh)\)
\(SA = 2(5 \cdot 3 + 5 \times 4 + 3 \times 4)\)
\(SA = 2(15 + 20 + 12)\)
\(SA = 2(47) = 94\)
Final Answer: 94 cm²
22
Triangular Prism: Base legs \(3\text{ ft}\), \(4\text{ ft}\) (\(hyp=5\text{ ft}\)), length \(10\text{ ft}\).
Step-by-Step Solution:
1. Two Triangular Bases:
\(2 \times (\frac{1}{2} \times 3 \times 4) = 12\text{ ft}^2\)
2. Three Rectangles:
\(3 \times 10 = 30\text{ ft}^2\)
\(4 \times 10 = 40\text{ ft}^2\)
\(5 \times 10 = 50\text{ ft}^2\)
3. Total Surface Area:
\(12 + 30 + 40 + 50 = 132\)
Final Answer: 132 ft²
Check for unit squared label representations (cm², ft²). Verify that students calculated all 5 faces for the triangular prism and all 6 faces for the rectangular prism before summing.
GEOMETRY WORKSHEET - ANSWER KEY Page 7 of 7
Part 4
length (l) width (w) height (h)
Prisms have 6 rectangular faces.
Opposite faces are identical in area!
SA = 2(lw) + 2(lh) + 2(wh)
Model Calculation:
Given a box with l = 5, w = 3, and h = 4:
1. Base areas (2 × lw): 2 × (5 × 3) = 30
2. Front/Back (2 × lh): 2 × (5 × 4) = 40
3. Side areas (2 × wh): 2 × (3 × 4) = 24
Total Sum (SA): 30 + 40 + 24 = 94 cm²
Grade 7 Geometry Classroom Pack Slide 5 of 7
Part 4 (Continued)
base (b=3) height (h=4) length (L=10) hyp = 5
Triangular prisms have 5 faces.
2 triangular bases + 3 rectangular panels!
Calculate the area of **each of the 5 faces** and sum them together. Do not forget that the two triangular bases are identical!
Model Calculation (shown left):
1. Two Triangle Bases: 2 × (½ × 3 × 4) = 12
2. Bottom Rectangle: 3 × 10 = 30
3. Vertical Side Rectangle: 4 × 10 = 40
4. Slanted Side Rectangle: 5 × 10 = 50
Total Sum (SA): 12 + 30 + 40 + 50 = 132 ft²
Grade 7 Geometry Classroom Pack Slide 6 of 7
Part 5
Decoding Strategy
Example: "Fabric needed to cover a triangular tent" tells you to find **Triangular Prism Surface Area**.
Worksheet Launch
Ready to Solve! Let's Begin.
Grade 7 Geometry Classroom Pack Slide 7 of 7
