Lesson 5.85.8 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can find the surface area of a pyramid by adding the base area and the lateral faces — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| PyramidSpanish: Pirámide | A solid with a flat bottom and triangle sides that meet at one point on top. | square base + 4 triangles |
| Slant heightSpanish: Altura inclinada (apotema) | The height of a side triangle, measured along its slanted face. | used in ½ × b × slant |
| Lateral faceSpanish: Cara lateral | A triangle side of a pyramid, not the bottom. | 4 on a square pyramid |
| BaseSpanish: Base | The flat bottom of a pyramid. | the square on the net |
| ApexSpanish: Ápice | The point at the top of a pyramid where the sides meet. | tip of the pyramid |
| Lateral areaSpanish: Área lateral | The total area of just the side triangles, not the bottom. | For a square pyramid: lateral area = 4 × (½ × base edge × slant height) |
How it worksWorked examplesurface area of a square pyramid
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A square pyramid has a base 10 cm on each side. Each triangular face has a slant height of 12 cm. Find the surface area.
- The net is a square base with 4 congruent triangles, one on each side.
- Area of the square base. 10 × 10 = 100
- One triangular face uses the slant height. ½ × 10 × 12 = 60
- Four faces plus the base. 60 × 4 = 240, then 240 + 100 = 340
Answer: The surface area is 340 square centimeters (340 cm²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A square pyramid has a base 14 in. on each side and a slant height of 9 in. Find the surface area.
- Sketch the net. Square: Triangles:
- Area of the square base. × = in²
- One triangular face. ½ × × = in²
- All the faces. × = , then + = in²
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The base is a with an area of .
- Each triangular face has a base of and a slant height of .
- There are triangular faces, so together they cover .
- The surface area is because I added .
Word bank pyramidbaseslant heightlateral faceapextrianglesquarecongruentaddsurface areasquare unitsnet
Watch outA common mistake
A common mistake in Surface Area of Pyramids is finding the four triangular lateral faces correctly (½ × base edge × slant height, times 4) and then stopping — forgetting to add the base area at the end. This leaves the total surface area too small by exactly the base's area. Before you submit, ask: 'Did I add the base area to the four lateral faces, or did I stop after the sides?'
Lesson 5.85.8 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can find the surface area of a pyramid by adding the base area and the lateral faces — one step at a time, with support.
-
1Complete each step, then write the final answer.
The net: 1 square base and 4 triangle faces. A square pyramid has a base that is 5 m by 5 m. Its slant height is 6 m. Find its surface area.
- 1What is the area of the base?
- 2What is the area of one triangle face?
- 3What is the area of all 4 triangle faces?
- 4Add the base. What is the surface area?
Final answer: -
2Complete each step, then write the final answer.
The net: 4 equal triangles. A pyramid has a triangle base. All 4 of its faces are the same triangle, with a base of 6 cm and a height of 5.2 cm. Find its surface area.
- 1What is the area of one triangle face?
- 2How many faces does this pyramid have, counting the base?
- 3Multiply. What is the surface area?
Final answer: -
3Complete each step, then write the final answer.
A square pyramid has a base that is 2 in by 2 in. Its slant height is 4 in. Find its surface area.
Show your workHint Find the base. Then find one triangle face and multiply by 4.
Final answer: -
4Complete each step, then write the final answer.
A square pyramid has a base that is 10 ft by 10 ft. Its slant height is 13 ft. Find its surface area.
Show your workHint Each triangle face has a base of 10 ft and a height of 13 ft.
Final answer: -
5Complete each step, then write the final answer.
A paperweight is a square pyramid. Its base is 3 cm by 3 cm. Its slant height is 5 cm. How much area must be polished on all its faces?
Show your workHint All its faces means the base and the 4 triangles.
Final answer: -
6Complete each step, then write the final answer.
A square pyramid has a base edge of 8 in and a slant height of 6 in. Ty writes 4 × (8 × 6) + 64 = 256. What is the correct surface area?
Show your workHint Check how Ty found each triangle face. What is the area of a triangle?
Final answer:
Explain your thinkingWhy do we use the slant height for the triangle faces? Why must we add the base too?
Sentence starter We use the slant height because ___. · We add the base because ___.