This can be tricky, but don’t be scared. Let go. So, the area of the entire figure, a trapezoid, is 48 square units. “What’s a trapezoid?” some of you ask. A trapezoid is simply any quadrilateral that has at least one set of parallel sides. Some say a trapezoid has ONLY one pair of parallel sides, but this minor debate is not material to our problem. “So, how do you calculate the area of a trapezoid?” is the next natural question. Well, being similar to a rectangle, you may have the inkling that length times width is involved, and you’re on the right track. Let’s say the lengths of the two parallel sides are an and b. Now, imagine drawing a line segment perpendicular to both a and b with endpoints on those sides. This segment is the height, h, of the trapezoid. The area of the trapezoid is thus given as: A = (a + b) / 2 * h This makes sense because you could think of stretching such a shape into a rectangle, whole length would be the average of a and b. Now, in order to find the area of the two triangles, we first need to find the length of x. 4x is one of our parallel side lengths, along with 8. And the height is 4. Let’s find x: A = (a + b) / 2 * h 48 = (8 + 4x) / 2 * 4 (4x + 8) * 2 = 48 4x + 8 = 24 4x = 16 x = 4 Alright, x=4. Now, we have two triangles, one with base x and height 4. The other has base 2x and height 4. Let’s calculate the areas: A1 = (1/2)b1*h AND A2 = (1/2)b2*h A1 = (1/2) * x * 4 AND A2 = (1/2) * 2x * 4 A1 = (1/2) * 4 * 4 AND A2 = (1/2) * 2 * 4 * 4 A1 = 2 * 4 AND A2 = 1 * 4 * 4 A1 = 8 AND A2 = 16 So the areas of the two triangles are 16 and 8, combining for 24, which is half the trapezoid.
Sometimes you complicate the process. Typical math teacher. No insult intended.
Can you work one on one withchild
given: b1 = 8
b2 = 4x
h = 4
Area Trapezoid :
A = 1/2 (b1 + b2) h
48 = 1/2 (8 + 4x) 4
48 = 2 (8 + 4x)
48 = 16 + 8x
48 - 16 = 16 - 16 + 8x
32 = 8x
32/8 = 8x/8
4 = x
b2 = 4x -> 4 · 4 = 16
Area Shaded triangle on the left:
b · h / 2
2x · 4 / 2
2(4) · 4 / 2
32 / 2 = 16✅
Area Shaded triangle on the right:
b · h / 2
x · 4 / 2
4 · 4 / 2 = 8✅
Area unshaded (trapezoid):
1/2(b1 + x ) h
1/2(8 + 4 ) 4
2(8 + 4) = 24
proof : area shaded triangle left + Area unshaded (trapezoid) + Area Shaded triangle right
Tot. A = 16 + 24 + 8 = 48
Do you go live so you can answer some questions and also do you have any a website where you can talk and work with the kids
It's in the description.
X = 4 and tris are 16 & 8 trap = 1/2 (B1 + B2) X H tri = 1/2 (B X H) thanks for the fun
This can be tricky, but don’t be scared. Let go.
So, the area of the entire figure, a trapezoid, is 48 square units. “What’s a trapezoid?” some of you ask. A trapezoid is simply any quadrilateral that has at least one set of parallel sides. Some say a trapezoid has ONLY one pair of parallel sides, but this minor debate is not material to our problem.
“So, how do you calculate the area of a trapezoid?” is the next natural question. Well, being similar to a rectangle, you may have the inkling that length times width is involved, and you’re on the right track. Let’s say the lengths of the two parallel sides are an and b. Now, imagine drawing a line segment perpendicular to both a and b with endpoints on those sides. This segment is the height, h, of the trapezoid. The area of the trapezoid is thus given as:
A = (a + b) / 2 * h
This makes sense because you could think of stretching such a shape into a rectangle, whole length would be the average of a and b.
Now, in order to find the area of the two triangles, we first need to find the length of x. 4x is one of our parallel side lengths, along with 8. And the height is 4. Let’s find x:
A = (a + b) / 2 * h
48 = (8 + 4x) / 2 * 4
(4x + 8) * 2 = 48
4x + 8 = 24
4x = 16
x = 4
Alright, x=4. Now, we have two triangles, one with base x and height 4. The other has base 2x and height 4. Let’s calculate the areas:
A1 = (1/2)b1*h AND A2 = (1/2)b2*h
A1 = (1/2) * x * 4 AND A2 = (1/2) * 2x * 4
A1 = (1/2) * 4 * 4 AND A2 = (1/2) * 2 * 4 * 4
A1 = 2 * 4 AND A2 = 1 * 4 * 4
A1 = 8 AND A2 = 16
So the areas of the two triangles are 16 and 8, combining for 24, which is half the trapezoid.
The axis 8 I mean is x = 8
Thank you. 24
Cool
24
Please help me
What do you need to know?