# ACT Math 5.2 Plane Geometry

ACT Math: Plane Geometry Drill 5, Problem 2. What is the area of the shaded sections?

ACT Math | Plane Geometry |

ACT Mathematics | Plane Geometry |

Area and Volume | Area |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Language | English Language |

Plane Geometry | Area Relations of plane figures |

Product Type | ACT Math |

### Transcript

At first, we may only see 6 itty-bitty equilateral triangles... but on second glance, we see

that there are, in fact, 2 big honkin' equilateral triangles here.

So we know the side length of the biggies...

and no matter which way we look at it, each side of the big triangles is cleanly cut into

thirds. Since the big sides all measure 6 units, each

third measures 2 units. These thirds make up the sides of the smaller triangles, which

are equilateral

We have the base -- 2 -- but we still need to find the height.

To do that, we split the small triangle in half and use the Pythagorean theorem... a

squared plus b squared equals c squared... to solve for the height. It looks something

like this: We add 1 squared plus x squared to equal 2

squared, and by solving for x, we get the square root of three.

The area of a triangle is 1/2 times the base times the height 2 times the

square root of three times one half... we get square root of three as the area of the

small triangle. Since there

are six small triangles, we have to multiply the square root of three by six and that gives us 6 root three.

The correct answer is D.