# Questions tagged [area]

Area is a quantity that expresses the extent of a two-dimensional measurement of a shape.

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### Area of a decreasing positive function

Suppose we have a decreasing positive function from 0 to infinity. Now suppose that it starts from somewhere on the y axis, something like f(0)=a, where a is a positive real. Can we say that the area ...
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### Find the colored area, tha triangle is a regular one [closed]

The task is to find the colored area, expressed with x (as a function of x). The triangle has a side length named x. We drew its altitudes and we circled from each corner with two different radius. ...
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### How to solve the problems in which wire is cut into 2 parts

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle ...
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### Surface area of quarter of a Sphere

A quarter sphere with a radius of $10 \text{ units}$. Please help, also remember the sides. I used the normal formula of the total surface area of a sphere and divided it by $4$, then added half the ...
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### In triangle $ABC$, $AA_1$, $BB_1$, $CC_1$ divide sides in ratio of $1: 2$ and meet at $M$, $K$, $L$. Find area relation of $KLM$ and $ABC$

Points $A_1$, $B_1$, $C_1$ divide sides $BC$, $CA$, $AB$ equilateral triangle $ABC$ in a ratio of $1: 2$. The line segments $AA_1$, $BB_1$, $CC_1$ determine the triangle $KLM$. Is the triangle $KLM$ ...
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### Illusion in maths?? (Area of sectors and segments) [closed]

I was practising for my maths Olympiad when I stumbled upon this question... This question is more than just a figure. It actually isn't what it looks like. I could've simply seen the solution at the ...
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### Surface Area of Cap below, Top Part of Sphere

How do I find the Surface Area of an oval cap below (Top of sphere)? Oval Cape Internet is stating: 2πRh However, a simple 8 radius circle is ...
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### What is area of shaded region?

Suppose the side length $a$ of the square is 10mm. A circle is tangent to all four sides of the square. And two quarter-circles with the same radius of 10mm have centers on the opposite vertices. It ...
This is a popular problem spreading around. Solve for the shaded reddish/orange area. (more precisely: the area in hex color #FF5600) $ABCD$ is a square with a side of $10$, $APD$ and $CPD$ are ...
### Calculating the area under the curve $e^x$ without calculus
I was thinking about the integral $$\int_{0}^{1}e^xdx$$ This is a problem that can be solved in seconds using calculus: the answer is $e-1$. But, I was wondering, is there a way of solving this ...