Area Architect Worksheet
Geometry Studio Level 1 & 2 Scaffolded
Area Architect Worksheet
Name:
Date:
Period:
Blueprint Formula Reference Always identify the perpendicular height (\(h \perp b\))!
Square 4 equal sides
\(A = s^2\) or \(s \times s\)
Rectangle Opposite sides =
\(A = b \times h\)
Triangle Half a rect.
\(A = \frac{1}{2}(b \times h)\)
Trapezoid 2 parallel bases
\(A = \frac{b_1 + b_2}{2} \times h\)
1
Phase 1: Step-by-Step Guided Calculation
Identify the values, substitute them into the formula, and calculate the total area with units squared.
Problem 1: Square Patio Tile
Side length \(s = 7\text{ cm}\)
7 cm 7 cm
Formula: \(A = s \times s\)
Substitute: \(A =\) _______ \(\times\) _______
Area =
\(\text{cm}^2\)
Problem 2: Solar Panel
Base \(b = 8\text{ m}\), Height \(h = 5\text{ m}\)
8 m 5 m
Formula: \(A = b \times h\)
Substitute: \(A =\) _______ \(\times\) _______
Area =
\(\text{m}^2\)
Problem 3: Roof Truss
Base \(b = 12\text{ ft}\), Height \(h = 6\text{ ft}\)
12 ft h = 6
Formula: \(A = \frac{1}{2}(b \times h)\)
Substitute: \(A = \frac{1}{2}(\) _____ \(\times\) _____ \()\)
Area =
\(\text{ft}^2\)
Problem 4: Garden Plot
\(b_1 = 5\text{ m}, b_2 = 11\text{ m}, h = 4\text{ m}\)
5 m 11 m 4 m
Formula: \(A = \frac{b_1 + b_2}{2} \times h\)
Substitute: \(A = \frac{\text{__} + \text{__}}{2} \times\) ____
Area =
\(\text{m}^2\)
2
Phase 2: Slant-Height Trap Filter
Architect Caution: Slanted sides are NOT heights! Cross out the decoy measurement you don't need, then calculate.
Problem 5: Triangular Pennant Watch Decoy!
Base = 10 in h = 8 in slant = 9 in
Cross out decoy side: ______
Show Calculation:
Area:
\(\text{in}^2\)
Problem 6: Canal Cross-Section Watch Decoy!
\(b_1 = 6\text{ ft}\) \(b_2 = 14\text{ ft}\) \(h = 7\text{ ft}\) slant = 8
Cross out decoy side: ______
Show Calculation:
Area:
\(\text{ft}^2\)
Unit 4: 2D Geometry & Measurement Page 1 of 2 Area of Triangles, Rectangles, Squares & Trapezoids
Geometry Studio Independent Application & Field Work
Area Architect Worksheet
Student:
Score: _____ / 20
3
Phase 3: Independent Shape Calculations
Write the formula, show your algebraic substitution, and calculate each area with units.
7. Square Window Pane
Each edge measures \(9.5\text{ inches}\)
9.5 in
Show Work:
Answer:
\(\text{in}^2\)
8. Right-Triangle Sail
Base = \(14\text{ m}\), Vertical Height = \(9\text{ m}\)
14 m 9
Show Work:
Answer:
\(\text{m}^2\)
9. Basketball Court Zone
Length = \(16\text{ yd}\), Width = \(7.5\text{ yd}\)
16 yd
Show Work:
Answer:
\(\text{yd}^2\)
10. Stage Ramp Surface
\(b_1 = 8\text{ ft}, b_2 = 18\text{ ft}, h = 6\text{ ft}\)
8 ft 18 ft
Show Work:
Answer:
\(\text{ft}^2\)
4
Phase 4: Community Park Blueprint
Composite Design
The town recreation center plans to build a community plaza composed of two sections: a Trapezoidal Stone Patio (Section A) and an adjacent Triangular Flower Garden (Section B).
Patio (A) h = 7 m \(b_1 = 10\text{ m}\) \(b_2 = 12\text{ m}\) Garden (B) \(b = 7.5\text{ m}\) \(h = 7\text{ m}\)
a. Area of Stone Patio (Section A):
\(A = \frac{10 + 12}{2} \times 7 =\) ______________________ \(\text{m}^2\)
b. Area of Flower Garden (Section B):
\(A = \frac{1}{2}(7.5 \times 7) =\) ______________________ \(\text{m}^2\)
c. Total Plaza Area (A + B):
\(\text{m}^2\)
Architect Self-Check: Rate your confidence with these four 2D formulas:
1 - Need Help 2 - Getting There 3 - Master Architect
Unit 4: 2D Geometry & Measurement Page 2 of 2 Area of Triangles, Rectangles, Squares & Trapezoids
