Grade 10 · Core Mathematics · Lesson 10 of 12

Determining Area of Irregular Polygons in Real Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Area of Polygons. In it, learners partition real-world irregular shapes such as church walls and window frames into simpler geometric shapes.

Strand Measurements and GeometrySub-strand Area of PolygonsLesson code 10CM-25-L1040 minutes · 2 slides

KICD learning outcome (f)

Determine the area of irregular polygons in different situations.

By the end of this lesson, learners should be able to

Partition real-world irregular shapes such as church walls and window frames into simpler geometric shapes.
Apply right-angled trigonometry and the trigonometric area formula $\frac{1}{2} a b \sin C$ to determine missing dimensions and calculate total surface areas of complex polygonal networks.

Key vocabulary

Composite shape: A geometric figure formed by combining two or more basic polygons together.; The hall window was modelled as a composite shape of a rectangle and triangle.
Polygonal network: An arrangement of connected polygons sharing common boundary line segments or vertices.; The spider web formed a polygonal network divided into small adjacent triangular sections.

Lesson preview

Slide 1 · Area of Architectural Composite ShapesModel · 18 min

Figure 1: A composite polygon representing a church wall, consisting of a triangular roof above a trapezium base.

Irregular polygons in architectural designs, such as church walls and hall window frames, often consist of composite structures. To find the surface area of such complex real-life shapes, we divide the polygon into standard geometric figures like trapeziums, rectangles, and triangles. We calculate the individual area of each component using relevant geometric formulas, then sum these sub-areas to determine the total enclosed surface area accurately.

Identify composite real-world structures like church walls by partitioning them into simpler geometric regions.
Use standard formulas to compute component areas for rectangles, trapeziums, and non-right-angled triangles.
Ensure adjacent boundary segments match correctly when evaluating sub-shapes of an irregular figure.
Sum all component areas to determine the overall surface area of the irregular polygon.

Worked example. Subdivide the wall along

C D

into trapezium

A B C D

(below) and triangle

C D E

(above). Calculate trapezium area:

{Area}_{1} = 0.5 \times (18 + 12) \times 8 = 120 m^{2}

. Calculate triangle area using

0.5 a b \sin C

{Area}_{2} = 0.5 \times D C \times C E \times \sin (40^{\circ}) = 0.5 \times 12 \times 10 \times \sin (40^{\circ}) = 60 \times 0.642788 = 38.5673 m^{2}

. Sum the component areas:

Total Area = 120 + 38.5673 = 158.5673 \approx 158.57 m^{2}

. Answer: $158.57 m^{2}$ .

Check question: A hall window is shaped as a composite polygon with a rectangular base measuring $4 m$ by $3 m$ and a triangular top with a base of $4 m$ and a height of $2.5 m$ . What is its total surface area?

$17 m^{2}$
$22 m^{2}$
$11 m^{2}$
$12 m^{2}$

Show answer

$17 m^{2}$ . The area of the rectangular base is $4 \times 3 = 12 m^{2}$ . The area of the triangular top is $0.5 \times 4 \times 2.5 = 5 m^{2}$ . The total area is the sum of these two regions: $12 + 5 = 17 m^{2}$ .

Slide 2 · Area of Multi-Region Polygonal NetworksPractice · 22 min

Figure 2: A rectangular shape that has been divided into two right-angled triangles by a diagonal line.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

Both slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 11 lessons in this sub-strand

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