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This document contains 9 multi-part geometry problems involving properties such as parallel and perpendicular lines, ratios of lengths and areas, and finding unknown values based on given information. Diagrams are provided with each problem to illustrate the geometric relationships.

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MCH
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© © All Rights Reserved
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87 views3 pages

cs3 PDF

This document contains 9 multi-part geometry problems involving properties such as parallel and perpendicular lines, ratios of lengths and areas, and finding unknown values based on given information. Diagrams are provided with each problem to illustrate the geometric relationships.

Uploaded by

MCH
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1. In the diagram, ABCD is a parallelogram.

Given that OC = 4 cm, O X̂D = 90° and the area of


∆BCD = 12 cm2, the length of DX in cm is:
(a) 4 (b) 12 (c) 8 (d) 3 (e) 48 ( )

D C

O
X

A B

2. In the diagram, PQRS is a parallelogram. Given that M and N are the mid–points of PQ and QR
Area of the 3 QMN
respectively, the value of Area of PQRS
is:
(a) 14 (b) 16 (c) 18 1
(d) 10 1
(e) 12 ( )

S R

P Q
M

3. In the diagram, PQ is parallel to BC, QR is parallel to AB, and BR : RC = a : b. Find the ratio of the
area of ∆PQR to the area of ∆ABC.
A
(a) a² : (a + b)²
(b) ab : (a + b)²
(c) ab : 2 (a + b)² P Q

(d) 2ab : (a + b)²


(e) ab : (a² + b²) ( )
B R C

4. If each edge of a cube is increased by 140%, the percentage increase in the surface area is:
(a) 176 (b) 276 (c) 376 (d) 476 (e) 576 ( )
5 In the diagram, ABCD is a parallelogram. If YZ = 12 AB, what fraction of the area of ABCD is the area
of ∆XYZ?
(a) 12 (b) 13 (c) 14 (d) 15 (e) 16 ( )

D Y Z C

A X B

6 In the diagram, PQRS is a trapezium in which SR is parallel to PQ. Given that SR = 5 cm,
RQ = 7 cm, PQ = 12 cm, and the area of ∆PQR is 21 cm², the area of ∆SQR is:
(a) 15 cm² (b) 8 43 cm² (c) 12 14 cm² (d) 50 52 cm² (e) 36cm² ( )

5 cm
S R

7 cm

P Q
12 cm

7 In the diagram, AB // CD // YZ. If XA = 2 cm, AC = 4 cm, CY = 6cm and the area of ∆XYZ is 54 cm²,
then the area of the shaded region is:
(a) 27 cm² (b) 18 cm² (c) 20 14 cm² (d) 12 cm² (E) 24cm² ( )
X

2
A B

C D

Y Z
8. In the diagram, triangles ABC and PQR are similar, PQ = 6 cm, and AB = 3cm. If the area of ∆PQR
is 40 cm², the area of ∆ABC is:
(a) 80 cm² (b) 18 cm² (c) 8 cm² (d) 10 cm² (e) 20 ( )
P

A
6 cm
3 cm

Q B

9. In the diagram, ABCD is a trapezium in which AB : CD = 2 : 5. If the area of ∆CDE is 75 cm², then
the area of ABCD is:
(a) 100 cm² (b) 147 cm² (c) 195 cm² (d) 300 cm² (e) 317 cm² ( )
A B

C D

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