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Question
Construct the following quadrilaterals with the given measurements and also find their area.
AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°
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Solution
AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°
Steps:
1. Draw a line segment AG = 4.5 cm
2. At G on AG made ∠AGX = 110°
3. With G as centre drawn an arc of radius 3.8 cm let it cut GX at R.
4. At R on GR made ∠GRZ = 90°
5. At A on AG made ∠GAY = 90°
6. AY and RZ meet at I.
7. AGRI is the required quadrilateral.
Calculation of Area:
Area of the quadrilateral AGRI = `1/2 xx "d" xx ("h"_1 + "h"_2) "sq.units"`
= `1/2 xx 6.8 xx (2.9 + 2.4) "cm"^2`
= `1/2 xx 6.8 xx 5.3 xx "cm"^2`
Area of the quadrilateral = 18.02 cm2
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