Area of shapes - class-VII
Calculate areas of rectangles, triangles, squares, circles, and composite shapes including optimization problems and unit conversions.
Questions
The area of a rectangle of length (x + 2) units and breadth (x -8) units is
- $x^2-16$
- $x^2-6x-16$
- $x^2-10x+16$
- $x^2-10$
A closed box made of steel of uniform thickness has length breadth and height 12 dm, 10 sm and 8 dm respectively If the thickness of the steel sheet is 1 dm then the inner surface area is
- $ \displaystyle 456$ $\displaystyle dm^{2}$
- $ \displaystyle 376$ $\displaystyle dm^{2}$
- $ \displaystyle 264$ $\displaystyle dm^{2}$
- $ \displaystyle 696$ $\displaystyle dm^{2}$
The side of a square is 2 cm Semicircles are constructed on two sides of the square then the area of the whole figure is
- $ \displaystyle (4+\pi )cm^{2} $
- $ \displaystyle (4+4\pi )cm^{2} $
- $ \displaystyle 4\pi cm^{2} $
- $ \displaystyle 8\pi cm^{2} $
A square of side x is taken A rectangle is cut out from this square such that one side of the rectangle is half that of the square and the other is $\displaystyle \frac{1}{3}$ of the first side of the rectangle
What is the area of the remaining portion?
- $\displaystyle \left ( \frac{3}{4} \right )x^{2}$
- $\displaystyle \left ( \frac{7}{8} \right )x^{2}$
- $\displaystyle \left ( \frac{11}{12} \right )x^{2}$
- $\displaystyle \left ( \frac{15}{16} \right )x^{2}$
Find the area of a triangle whose sides are 9 cm, 12 cm, and 15 cm.
- $34cm^2$
- $44cm^2$
- $54cm^2$
- $55cm^2$
Area bounded by $y|y|-x|x|=1,\ y|y|+x|x|=1$ and $y=|x|$ is
- $\dfrac{\pi}{2}$
- ${\pi}$
- $\dfrac{\pi}{4}$
- $None\ of\ these$
A farmer wishes to cultivate four different crops in equal areas in his $1$ car of land.. The land he should allocate for each crop is:
- $10\ m^{2}$
- $25\ m^{2}$
- $75\ m^{2}$
- $100\ m^{2}$
A room is x meters long, y meters broad, and z meters high; find how many square meters of carpet will be required for the floor and how many square meters of paper for the walls?
- xy and 2xy + 2yz
- xy and 2xz + 2yz
- xy and 2xy
- xy and 2xy + 2xz
Find the area of a square inscribed in a circle of radius $\displaystyle 5\sqrt{2}$ cm (in $\displaystyle cm^{2}$)
- 75
- 100
- 125
- 150
What is the maximum area of a four-sided plane with a perimeter of $12$ inches?
- $8$ square inches
- $10$ square inches
- $6$ square inches
- $9$ square inches
Calculate area of the shape obtained by joining an equilateral triangle to one of the end of rectangle and a semicircle to the other end of rectangle. The sides of equilateral triangle is $3$ cm and one of the sides of rectangle is $4$ cm.
- $28.12\ cm^{2}$
- $30.02\ cm^{2}$
- $35.02\ cm^{2}$
- $40.02\ cm^{2}$
Consider a rectangle of perimeter $24\ cm$ with sides $a$ and $b$. Then the total number of square grids formed in that rectangle is given by
- $a\times b$
- $a+b$
- $a-b$
- $\dfrac{a}{b}$
Form a rectangle with $8$ square grids where each square grid measure $1\ cm^{2}$. Find the total area of the rectangle.
- $8\ cm^{2}$
- $12\ cm^{2}$
- $16\ cm^{2}$
- $20\ cm^{2}$
Let there be a rectangle of area $24\ cm^{2}$. Then find the total number of square grids made in this rectangle.(Each square grid measures $1\ cm^{2}$)
- $3$
- $6$
- $12$
- $24$
Three coins of the same size (radius $1cm$) are placed on table such that each of them touches the other two. The area enclosed by the coins is:
- $\left( \cfrac { \pi }{ 2 } -\sqrt { 3 } \right) { cm }^{ 2 }$
- $\left( \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$
- $\left(2 \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$
- $\left(3 \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$