III gimnazjum

Matematyka 2001

Matematyka

Liczy się matematyka 3

Matematyka 2001. Zeszyt ćwiczeń cz. 1

Matematyka 2001. Zeszyt ćwiczeń cz. 2

Matematyka 3. Ćwiczenia podstawowe

Matematyka 3. Zeszyt zadań

Matematyka na czasie! 3

Matematyka wokół nas 3

Matematyka wokół nas 3. Zeszyt ćwiczeń cz. 1

Matematyka wokół nas 3. Zeszyt ćwiczeń cz. 2

Matematyka z plusem 3

Matematyka z plusem 3. Zbiór zadań 2001

Policzmy to razem 3

Pole prostokąta obliczamy korzystając z&nbsp; wzoru: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9dd8d202f4cd5fddf9be8e2a822d8fe903ba0323972dbb4e415e4c8f5345b469_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9dd8d202f4cd5fddf9be8e2a822d8fe903ba0323972dbb4e415e4c8f5345b469_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4a479db6af79906e7200f9560d9af890f0077e394e3ae44cbd2a2bb3ba5c2c2d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4a479db6af79906e7200f9560d9af890f0077e394e3ae44cbd2a2bb3ba5c2c2d_big.svg" type="image/svg+xml"></object> &nbsp;- długości boków tego prostokąta <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9e51c14dfb51f69ac64302ad0323ac62a121d524871c46065e8282b280be07f9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9e51c14dfb51f69ac64302ad0323ac62a121d524871c46065e8282b280be07f9_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ef0dbf63451c93925a70aeb21648a78e09ea79de16de8f241d7c8b0a1d2f410d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ef0dbf63451c93925a70aeb21648a78e09ea79de16de8f241d7c8b0a1d2f410d_big.svg" type="image/svg+xml"></object> &nbsp; zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/a2091d93b5f485d0982b17ddf10601c06a846f5277bcc6713809b305318efa2f_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/a2091d93b5f485d0982b17ddf10601c06a846f5277bcc6713809b305318efa2f_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/70b2d24241c29d7fda4a997486fe679a0e3cab68fc9821ce0d913ed24b5da6df_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/70b2d24241c29d7fda4a997486fe679a0e3cab68fc9821ce0d913ed24b5da6df_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4d21817c3224ecb24d4c46cfa143bce379880677f269289942345da25ccf10fc_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4d21817c3224ecb24d4c46cfa143bce379880677f269289942345da25ccf10fc_big.svg" type="image/svg+xml"></object> &nbsp; Odp.: C

Pole zacieniowanego trójkąta to różnica pól prostokąta o bokach b i a oraz sumy pól trzech trójkątów prostokątnych , zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f91707dc6b803ef820c2c2c15b94d3263d9702aeceb556ed26e4eaea07a3c1bb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f91707dc6b803ef820c2c2c15b94d3263d9702aeceb556ed26e4eaea07a3c1bb_big.svg" type="image/svg+xml"></object>

Obliczmy pole prostokąta o bokach długości a i b: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f9de323e719027ae620816daba50690bb354235a7a1295b8a64ed1e6fc2ce37f_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f9de323e719027ae620816daba50690bb354235a7a1295b8a64ed1e6fc2ce37f_big.svg" type="image/svg+xml"></object> &nbsp; Obliczmy pole prostokąta o bokach długości&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9822ee4a4b238f0601d13b02104bd8937e8537b8524564e580707d8026bc3ebc_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9822ee4a4b238f0601d13b02104bd8937e8537b8524564e580707d8026bc3ebc_big.svg" type="image/svg+xml"></object>

Wiemy, że: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/996726b7f97d72564e74ddb01cb0b5c7314f792e645b2df8f99bd93a934cc684_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/996726b7f97d72564e74ddb01cb0b5c7314f792e645b2df8f99bd93a934cc684_big.svg" type="image/svg+xml"></object> &nbsp; gdzie&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8254c329a92850f6d539dd376f4816ee2764517da5e0235514af433164480d7a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8254c329a92850f6d539dd376f4816ee2764517da5e0235514af433164480d7a_big.svg" type="image/svg+xml"></object> &nbsp;- jest liczba całkowitą zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/999dd96c3f7d955da0022f60d4ab73c77dfd0ce380c442c07af2d26507ee32b0_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/999dd96c3f7d955da0022f60d4ab73c77dfd0ce380c442c07af2d26507ee32b0_big.svg" type="image/svg+xml"></object>

W klasie 3a jest&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881_big.svg" type="image/svg+xml"></object> &nbsp;uczniów w tym&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/a1fce4363854ff888cff4b8e7875d600c2682390412a8cf79b37d0b11148b0fa_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/a1fce4363854ff888cff4b8e7875d600c2682390412a8cf79b37d0b11148b0fa_big.svg" type="image/svg+xml"></object>

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