Given:Parallelogram \( \mathrm{ABCD} \) and rectangle \( \mathrm{ABEF} \) are on the same base \( \mathrm{AB} \) and have equal areas.To do:We have to show that the perimeter of the parallelogram is greater than that of the rectangle.Solution:Parallelogram \( \mathrm{ABCD} \) and rectangle \( \mathrm{ABEF} \) are on the same ... Read More

Given:$AP \| BQ \| \mathrm{CR}$.To do:We have to prove that \( \operatorname{ar}(\mathrm{AQC})=\operatorname{ar}(\mathrm{PBR}) . \)Solution:$\triangle BQC$ and $\triangle BQR$ lie on the same base $BQ$ and between the parallels $BQ$ and $CR$.Therefore, $ar(\triangle BQR) = ar(\triangle BQC)$.....…(i)$\triangle AQB$ and $\triangle PBQ$ lie on the same base $BQ$ and between the parallels ... Read More

Given:Diagonals \( \mathrm{AC} \) and \( \mathrm{BD} \) of a quadrilateral \( A B C D \) intersect at \( O \) in such a way that ar \( (\mathrm{AOD})=\operatorname{ar}(\mathrm{BOC}) \).To do:We have to prove that \( \mathrm{ABCD} \) is a trapezium.Solution:$ar(\mathrm{AOD})=\operatorname{ar}(\mathrm{BOC})$Adding $ar(\triangle AOB)$ on both sides, we get, $ar(\triangle ... Read More

Given:A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he ... Read More

Given:\( \mathrm{ABCD} \) is a trapezium with \( \mathrm{AB} \| \mathrm{DC} \). A line parallel to \( \mathrm{AC} \) intersects \( \mathrm{AB} \) at \( \mathrm{X} \) and \( \mathrm{BC} \) at Y. To do:We have to prove that ar \( (\mathrm{ADX})=\operatorname{ar}(\mathrm{ACY}) \).Solution:$AC \| XY$Join $CX, AY$ and $DX$$\triangle ADX$ and ... Read More

Given:The length of the box $=1.5\ m$.The breadth of the box $=1.25\ m$.The height of the box $=65\ cm=0.65\ m$.To do:We have to find:(i) The area of the sheet required for making the box.(ii) The cost of sheet for it, if a sheet measuring \( 1 \mathrm{~m}^{2} \) costs Rs. ... Read More

Given: The length, breadth and height of a room are $5\ m, 4\ m$ and $3\ m$. respectively.To do: We have to find the cost of whitewashing the walls of the room and the ceiling at the rate of $\ Rs. 7.50\ per\ sq\ m$.Solution:The length, breadth and height of the room ... Read More

Given:The floor of a rectangular hall has a perimeter \( 250 \mathrm{~m} \) and the cost of painting the four walls at the rate of \( Rs. 10 \mathrm {per}\mathrm {m}^{2} \) is \( Rs. 15000 \).To do:We have to find the height of the hall.Solution:Let the length, breadth and ... Read More

Given:The paint in a certain container is sufficient to paint an area equal to $9.375\ m^2$. The dimensions of each brick is $22.5\ cm \times 10\ cm \times 7.5\ cm$.To do:We have to find the number of bricks that can be painted out of the container.Solution:Area of the place for painting ... Read More

Given:A cubical box has each edge \( 10 \mathrm{~cm} \) and another cuboidal box is \( 12.5 \mathrm{~cm} \) long, \( 10 \mathrm{~cm} \) wide and \( 8 \mathrm{~cm} \) high.To do:We have to find:(i) Which box has the greater lateral surface area and by how much and(ii) Which box ... Read More