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Similarity Mathematics - Similarity

ICSE - STD 10 - Mathematics (ICSE - English Medium). 47 questions in this chapter.

Question types

Similarity question types

47 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

47
Questions
5
Question groups
5
Question types
Sample Questions

Similarity questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1[1 Mark Question Answer]1 Mark
The scale of a map is $1 : 200000$. A plot of land of area $20\ km^2$​​​​​​​ is to be represented on the map. Find:
The area in $km^2​​​​​​​$​​​​​​​ that can be represented by $1\ cm^2$​​​​​​​
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Q 2[2 Mark Question Answer]2 Marks
The scale of a map is $1 : 200000$. A plot of land of area $20km^2$​​​​​​​ is to be represented on the map. Find
The area on the map that represents the plot of land.
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Q 3[2 Mark Question Answer]2 Marks
The scale of a map is $1 : 200000$. A plot of land of area $20km^2$​​​​​​​ is to be represented on the map. Find:
The number of kilometres on the ground represented by lcm or the map
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Q 7[3 marks sum]3 Marks
A model of a ship is made with a scale factor of 1 : 500. Find
The deck area of the model, if the deck area of the ship is $1500000 m^2$
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Q 9[3 marks sum]3 Marks
The dimensions of a buiIding are $50\ m$ Iong, $40\ m$ wide and $70\ m$ high. A model of the same building is made with a scale factor of $1: 500.$ Find the dimensions of the model.
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Q 10[3 marks sum]3 Marks
In Δ ABC, D and E are points on the sides AB and AC respectively. If AD= 4cm, DB=4.Scm, AE=6.4cm and EC=7.2cm, find if DE is parallel to BC or not.
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Q 11[5 marks sum]5 Marks
On a map drawn to a scale of $1 : 25000,$ a rectangular plot of land, $ABCD$ is measured as $AB= 12\ cm$ and $BC = 16\ cm.$ calculate the diagonal distance of the plot in km and the plot area in $km^2 .$
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Q 12[5 marks sum]5 Marks
On a map drawn to a scale of $1 : 25000,$ a triangular plot of a land is marked as $ABC$ with $AB= 6cm, BC = 8cm$ and $\angle ABC = 90^\circ.$ Calculate the actual length of $AB$ in km and the actual area of the plot in $km^2 .$
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Q 13[5 marks sum]5 Marks
Figure shows $\triangle PQR$ in which $ST \| QR$ and $SR$ and $QT$ intersect each other at $M$. If $\frac{ PT }{ TR }=\frac{5}{3}$ find $\frac{\operatorname{Ar}(\triangle MTS )}{\operatorname{Ar}(\triangle MQR )}$
Image
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Q 14[5 marks sum]5 Marks
In $\triangle ABC$, $DE \| BC$; $DC$ and $EB$ intersects at $F$. if $\frac{ DE }{ BC }=\frac{2}{7}$, find $\frac{\operatorname{Ar}(\triangle FDE )}{\operatorname{Ar}(\triangle FBC )}$
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Q 15[5 marks sum]5 Marks
Prove that the area of Δ BCE described on one side BC of a square ABCD is one half the area of the similar Δ ACF described on the diagonal AC.
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Q 16[4 marks sum]4 Marks
The actual area of an island is $1872$ $km^2 $. On a map, this area is $117$ $cm^2$. if the length of the coastline is $44\ cm$ on the map, find the length of its actual coastline.
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Q 17[4 marks sum]4 Marks
 An aeroplane is $30 \ m$ long and its model is $15 \ cm$ long. If the total outer surface area of the model is $150 cm^2$, find the cost of painting the outer surface of the aeroplane at Rs. $120$ per $m ^2$, if $50 m^2$ is left out for windows.
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Q 18[4 marks sum]4 Marks
Figure shows $\triangle K L M, P$ an $T$ on $K L$ and $K M$ respectively such that $\angle K L M=\angle K T P$.
If $\frac{ KL }{ KT }=\frac{9}{5}$, find $\frac{\operatorname{Ar} \triangle KLM }{\operatorname{Ar} \triangle KTP }$.
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Q 19[4 marks sum]4 Marks
$\text { In } \triangle ABC , MN \| BC \text {. }$
Image
If $BC =14 cm$ and $MN =6 cm$, find $\frac{\operatorname{Ar} \triangle AMN }{\text { Ar. (trapezium MBCN) }}$
$\text { In } \triangle ABC , MN \| BC \text {. }$
Image
If $BC =14 cm$ and $MN =6 cm$, find $\frac{\operatorname{Ar} \triangle AMN }{\text { Ar. (trapezium MBCN) }}$
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Q 20[4 marks sum]4 Marks
In $\triangle ABC , MN \| BC$.
Image

If $\frac{ AB }{ AM }=\frac{9}{4}$, find $\frac{\operatorname{Ar}(\text { trapezium } MBCN )}{\operatorname{Ar} .(\triangle ABC )}$
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