Transcript height - Haiku Learning

11-1 Areas of Triangles and
Parallelograms
Hubarth
Geometry
Postulate
Area of a Square Postulate
The area of a square is the length of its side squared
Area Congruence Postulate
If two polygons are congruent, then they have the same area
Area Addition Postulate
The area of a region is the sum of the area of its nonoverlapping parts.
Square all sides are equal and all angles are right angles.
Rectangle opposite sides are equal and all angles are right angles.
Theorem
Area of a Rectangle
The area of a rectangle is the product of its base and height.
h
b
A =bh
Parallelograms opposite side are congruent and opposite angles are congruent.
In a parallelogram either pair of sides can be used as the bases of the parallelogram. The
height is the perpendicular distance between the bases.
base
h height
b
base
Theorems
Area of a Parallelogram
The area of a parallelogram is the product of a base and its corresponding height.
A= bh
Theorem
Area of a Triangle
The area of a triangle is one half the product of a base and its corresponding height.
height
h
base
b
1
bh
A = bh or
2
2
Ex 1 Use a Formula to Find Area
Find the area of
Method 1
PQRS.
Use PS as the base.
The base is extended to measure the height RU.
b= 6 and h=8.
A = 6×8 = 48
Method 2
Use PQ as the base. Then the height
is QT. b=12 and h=4
A = 12×4 = 48
Ex 2 Solve for the Unknown Measures
The base of a triangle is twice its height. The area of the triangle is 36 square inches.
Find the base and height
Let h represent the height of the triangle. Then the
base is 2h.
bh
A=
2
h×2h
2
2h2
36 =
2
36 =
36 = h2
36 = h2
h=6
h=6 and b=2(6)=12
Ex 3 Solve a Multi-step Problems
You need to buy paint so that you can
paint the side of a barn. A gallon of paint
covers 350 square feet. How many
gallons should you buy?
You can use a right triangle and a rectangle to approximate the area of the
side of the barn.
First, find the base and height of the right triangle. It is an Isosceles triangle so the base
and height are the same. We will use the Pythagorean Theorem.
x 2 + x 2 = 262
2x 2 = 676
x 2 = 338
x = 18.4
Area of the right triangle =
Area = 169.3
18.4×18.4
2
Ex 3 continued
Second, find the area of the rectangle portion of the barn.
Area = 26×18=468
Third, find the area of the entire side of the barn.
Area = 468+169.3 = 637.3
Lastly, determine how many gallons of paint.
gallons =
637.3
= 1.82
350
So, you will need 2 gallons of paint
Practice
1. Find the perimeter and area of the polygon.
52 + h2 = 132
a.
25+ h = 169
2
b.
h2 = 144
h = 12
5×12
= 30
2
Perimeter = 5+12 +13 = 30
Area =
Area = 17(30) = 510
Perimeter = 20 + 20 + 30 + 30 = 100
2. A parallelogram has an area of 153 square inches and a height of 17 inches.
What is the length of the base?
153 = 17×b
b=9
3. WHAT IF? In Example 3, suppose there is a 5 foot by 10 foot rectangular
window on the side of the barn. What is the approximate area you need to paint?
Area of the window = 5(10)=50
637.3 – 50 =587.3