Samacheer Kalvi 8th Maths Guide Chapter 5 Geometry Ex 5.4

February 23, 2022

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 5 Geometry Ex 5.4

I. Construct the following quadrilaterals with the given measurements and also find their area.

Question 1.
ABCD, AB = 5 cm, BC = 4.5 cm, CD = 3.8 cm, DA = 4.4 cm and AC = 6.2 cm.
Answer:
Given ABCD, AB = 5 cm, BC = 4.5 cm, CD = 3.8 cm, DA = 4.4 cm and AC = 6.2 cm.

Steps:

Draw a line segment AB = 5 cm
With A and B as centers drawn arcs of radii 6.2 cm and 4.5cm respectively and let them cut at C.
Joined AC and BC.
With A and C as centrers drawn arcs of radii 4.4cm and 3.8 cm respectively and let them at D.
Joined AD and CD.
ABCD is the required quadrilateral.

Calculation of Area:
Area of the quadrilateral ABCD = 1/2 × d × (h₁1 + h₂) sq. units
= 1/2 × 6.2 × (2.6 + 3.6)cm² = 3.1 × 6.2 = 19.22 cm²

Question 2.
PLAY, PL = 7cm, LA = 6cm, AY = 6cm, PA = 8cm and LY = 7cm.
Answer:
Given PLAY, PL = 7cm, LA = 6cm, AY = 6cm, PA = 8cm and LY = 7cm

Steps:

Drawn a line segment PL = 7 cm
With P and L as centers, drawn arcs of radii 8 cm and 6 cm respectively, let them cut at A.
Joined PA and LA.
With L and A as centers, drawn arcs of radii 7 cm and 6 cm respectively and let them cut at Y.
Joined LY, PY and AY.
PLAY is the required quadrilateral.

Calculation of Area:
Area of the quadrilateral PLAY = 1/2 × d × (h₁ + h₂) sq. units = 1/2 × 8 × (5.1 + 1.4) cm²
1/2 × 8 × 6.5 cm² = 26 cm²
Area of the quadrilateral = 26 cm²

Question 3.
PQRS, PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q = 120°.
Answer:
Given PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q = 120°

Steps:

Draw a line segment PQ = 3.5 cm
Made ∠Q = 120°. Drawn the ray QX.
With Q as centre drawn an arc of radius 3.5 cm. Let it cut the ray QX at R.
With R and P as centres drawn arcs of radii 5.2cm and 5.5 cm respectively and let them cut at S.
Joined PS and RS.
PQRS is the required quadrilateral.

Calculation of Area:
Area of the quadrilateral PQRS = 1/2 × d × (h₁ + h₂) sq. units
= 1/2 × 6 × (4.3 + 17)cm²
= 3 × 6cm²
= 18 cm²
Area of the quadrilateral PQRS = 18 cm²

Question 4.
MIND, MI = 3.6 cm, ND = 4 cm, MD = 4 cm, ∠M = 50° and ∠D = 100°.
Answer:
Given MI = 3.6 cm, ND = 4 cm, MD = 4 cm, ∠M = 50° and ∠D = 100°

Steps:

Drawn a line segment MI = 3.6 cm
At M on MI made an angle ∠IMX = 500
Drawn an arc with center M and radius 4 cm let it cut MX it D
At D on DM made an angle ∠MDY = 100°
With I as center drawn an arc of radius 4 cm, let it cut DY at N.
Joined DN and IN.
MIND is the required quadrilateral.

Calculation of Area:
Area of the quadrilateral MIND = 1/2 × d × (h₁ + h₂) sq. units = 1/2 × 3.2 × (2.7 + 33) cm²
= 1/2 × 3.2 × 6 cm² = 9.6 cm²
Area of the quadrilateral = 9.6 cm²

Question 5.
AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°.
Answer:
AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°.

Steps:

Draw a line segment AG = 4.5 cm
At G on AG made ∠AGX = 110°
With G as centre drawn an arc of radius 3.8 cm let it cut GX at R.
At R on GR made ∠GRZ = 90°
At A on AG made ∠GAY = 90°
AY and RZ meet at I.
AGRI is the required quadrilateral.

Calculation of Area:
Area of the quadrilateral AGRI = 1/2 × d × (h₁ + h₂) sq. units = × 6.8 × (2.9 + 2.4) cm²
= 1/2 × 6.8 × 5.3 × cm²
Area of the quadrilateral = 18.02 cm²

II. Construct the following trapeziums with the given measures and also find their area.

Construction:
Steps:

Draw a line segment AI = 6cm.
With A and I as centres, draw arcs of radii 9 cm and 5 cm respectively and let them cut at M
Join AM and IM.
Draw MX parallel to AI
With M as centre, draw an arc of radius 6.5 cm cutting MX at S.
Join AS AIMS is the required trapezium.

Calculation of Area

Rough Diagram
Samacheer Kalvi 8th Maths Guide Answers Chapter 5 Geometry Ex 5.4 8

Construction:
Steps:

Draw a line segment CU = 7cm.
Construct an angle ∠UCE = 80° at C
With C as centre, draw an arc of radius 6 cm cutting CY at E
Draw EX parallel to CU
With E as centre, draw an arc 7 cm of radius 5 cm cutting EX at T
Join UT. CUTE is the required trapezium.

Calculation of area:
Area of the trapezium CUTE = 1/2 × h × (a + b) sq. units
= 1/2 × 5.9 × (7 + 5)sq. units
= 35.4 sq.cm

Construction:
Steps:

Draw a line segment AR = 7 cm.
Construct an angle ∠RAX = 100° at A
Construct an angle ∠ARN = 60° at R
With R as centre, draw an arc of radius 6.5 cm cutting RN at M
Draw MY parallel to AR
ARMY is the required trapezium.

Construction:
Steps:

Draw a line segment CI = 7 cm.
Mark a point D on CI such that CD = 4cm
With D and I as centres, draw arcs of radii 6 cm and 5.5 cm respectively.
Let them cut at T. Join DT and IT.
With C as centre, draw an arc of radius 6 cm.
Draw TY parallel to Cl. Let the line cut the previous arc at Y.
Join CY. CITY is the required trapezium.

Construction of area:
Area of the trapezium CITY = 1/2 × h × (a + b) sq. units
= 1/2 × 5.5 × (7 + 4)sq.units
= 1/2 × 5.5 × 11
= 30.25 sq.cm

SabDekho

The Complete Educational Website

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 5 Geometry Ex 5.4

You May Also Like

Leave a Reply Cancel reply