Grade 10 · Core Mathematics · Lesson 12 of 12

Applying Polygon Area Calculations in Real-Life Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Area of Polygons. In it, learners calculate the surface area of real-life kite-shaped objects using perpendicular diagonals or trigonometric area decomposition.

Strand Measurements and GeometrySub-strand Area of PolygonsLesson code 10CM-25-L1240 minutes · 2 slides

KICD learning outcome (g)

Explore the area of polygons as used in real-life situations.

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

Calculate the surface area of real-life kite-shaped objects using perpendicular diagonals or trigonometric area decomposition.
Determine the surface area of regular octagonal objects given side length or vertex-to-centre distance.
Solve practical cost estimation problems for tiling or constructing polygonal structures.

Key vocabulary

Kite: A quadrilateral with two distinct pairs of adjacent sides that are equal in length.; The area of a kite with diagonals $5.2 m$ and $3.6 m$ is $9.36 m^{2}$ .
Apothem: The perpendicular distance from the centre of a regular polygon to one of its sides.; The apothem of a regular octagonal hut floor of side $4 m$ is $4.83 m$ .

Lesson preview

Slide 1 · Area of Kite-Shaped Structures and Architectural FacadesModel · 18 min

Figure 1: A kite split into two isosceles triangles with given side lengths and angles to demonstrate how to calculate its total area.

Polygons appear frequently in practical applications, such as architectural windows fitted in halls, church wall designs, kitchen gardens, and decorated cakes. To find the surface area of a kite-shaped object, we can multiply perpendicular diagonals using $A = \frac{1}{2} d_{1} d_{2}$ or divide the kite into two isosceles triangles and apply the trigonometric area formula $A = \frac{1}{2} a b \sin C$ . Breaking complex shapes into standard triangles allows accurate measurement for materials and costs.

Kite structures in buildings, windows, and gardens can be split into triangles to find total area.
When perpendicular diagonals $d_{1}$ and $d_{2}$ are known, kite area is calculated using $A = \frac{1}{2} d_{1} d_{2}$ .
For kites with known side lengths and vertex angles, use the trigonometric area formula $\frac{1}{2} a b \sin C$ .
Decomposing complex architectural facades into basic polygons simplifies calculating total material requirements and construction costs.

Worked example. Split the kite along the cross diagonal

B D

into two isosceles triangles. (Check:

B D = 2 \times 0.8 \times \sin 30^{\circ} = 0.80 m

and

B D = 2 \times 1.4 \times \sin {16.6}^{\circ} = 0.80 m

, so the triangles fit together.) Calculate upper triangle area:

A_{1} = \frac{1}{2} \times 0.8 \times 0.8 \times \sin (60^{\circ}) = 0.32 \times 0.866025 = 0.277128 m^{2}

. Calculate lower triangle area:

A_{2} = \frac{1}{2} \times 1.4 \times 1.4 \times \sin ({33.2}^{\circ}) = 0.98 \times 0.547563 = 0.536612 m^{2}

. Sum the two triangle areas:

Total Area = 0.277128 + 0.536612 = 0.813740 \approx 0.814 m^{2}

. Answer: Total surface area = $0.814 m^{2}$ .

Check question: A kite-shaped kitchen garden has perpendicular diagonals measuring $4.8 m$ and $3.5 m$ . Calculate the area of the kitchen garden.

$4.15 m^{2}$
$4.2 m^{2}$
$8.4 m^{2}$
$16.8 m^{2}$

Show answer

$8.4 m^{2}$ . Using the kite area formula $A = \frac{1}{2} d_{1} d_{2}$ , the area is calculated as $\frac{1}{2} \times 4.8 \times 3.5 = 8.4 m^{2}$ .

Slide 2 · Area and Cost Calculations for Regular Octagonal StructuresPractice · 22 min

Figure 2: A regular octagon divided into eight congruent central isosceles triangles, with one highlighted to show its base, central angle, and apothem.

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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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Applying Polygon Area Calculations in Real-Life Situations

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

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 12 lessons in Area of Polygons